aiohttp.AsyncResolver needs to be created inside an async function
Despite the efforts in #681, I failed to realise `aiohttp.AsyncResolver` suffers from the same `DeprecationWarning` as the session. 

Thankfully, it seems that the resolver of a `aiohttp.TCPConnector` instance can be swapped out whenever. It just uses whatever the value of `self._resolver` is every time it needs to resolve a host. It is a "private" attribute but ostensibly there isn't any reason it shouldn't be changed. 

So, the resolver can simply be created in `Bot.start()`. I believe it is safe to also close the resolver and even the connector in `Bot.close()`. I was mainly concerned by how discord.py would handle this. The connector goes to discord.py's `HTTPClient` which uses it to create an internal `aiohttp.ClientSession` - basically the same thing we use the connector for. Whenever `Client.clear()` is called, the session gets recreated using `HTTPClient._connector`. Therefore, the connector can be re-created and assigned to that attribute before `Client.clear()` is called.

Recreating the connector would be a bit clumsy. For `HTTPClient`, the `Bot.http._connector` attribute needs to be assigned the new connector instance. For `APIClient`, the `Bot.APIClient._session_args` dictionary needs to be updated with the new connector instance. I think the latter could benefit from allowing kwargs to be passed to `recreate()`, which will override the "default" `_session_args`.
diff --git a/bot/api.py b/bot/api.py
index e5991611..4b852058 100644
--- a/bot/api.py
+++ b/bot/api.py
@@ -52,7 +52,7 @@ class APIClient:
 
         self._ready = asyncio.Event(loop=loop)
         self._creation_task = None
-        self._session_args = kwargs
+        self._default_session_kwargs = kwargs
 
         self.recreate()
 
@@ -60,25 +60,41 @@ class APIClient:
     def _url_for(endpoint: str) -> str:
         return f"{URLs.site_schema}{URLs.site_api}/{quote_url(endpoint)}"
 
-    async def _create_session(self) -> None:
-        """Create the aiohttp session and set the ready event."""
-        self.session = aiohttp.ClientSession(**self._session_args)
+    async def _create_session(self, **session_kwargs) -> None:
+        """
+        Create the aiohttp session with `session_kwargs` and set the ready event.
+
+        `session_kwargs` is merged with `_default_session_kwargs` and overwrites its values.
+        If an open session already exists, it will first be closed.
+        """
+        await self.close()
+        self.session = aiohttp.ClientSession(**{**self._default_session_kwargs, **session_kwargs})
         self._ready.set()
 
     async def close(self) -> None:
         """Close the aiohttp session and unset the ready event."""
-        if not self._ready.is_set():
-            return
+        if self.session:
+            await self.session.close()
 
-        await self.session.close()
         self._ready.clear()
 
-    def recreate(self) -> None:
-        """Schedule the aiohttp session to be created if it's been closed."""
-        if self.session is None or self.session.closed:
+    def recreate(self, force: bool = False, **session_kwargs) -> None:
+        """
+        Schedule the aiohttp session to be created with `session_kwargs` if it's been closed.
+
+        If `force` is True, the session will be recreated even if an open one exists. If a task to
+        create the session is pending, it will be cancelled.
+
+        `session_kwargs` is merged with the kwargs given when the `APIClient` was created and
+        overwrites those default kwargs.
+        """
+        if force or self.session is None or self.session.closed:
+            if force and self._creation_task:
+                self._creation_task.cancel()
+
             # Don't schedule a task if one is already in progress.
-            if self._creation_task is None or self._creation_task.done():
-                self._creation_task = self.loop.create_task(self._create_session())
+            if force or self._creation_task is None or self._creation_task.done():
+                self._creation_task = self.loop.create_task(self._create_session(**session_kwargs))
 
     async def maybe_raise_for_status(self, response: aiohttp.ClientResponse, should_raise: bool) -> None:
         """Raise ResponseCodeError for non-OK response if an exception should be raised."""
diff --git a/bot/bot.py b/bot/bot.py
index 19b9035c..950ac675 100644
--- a/bot/bot.py
+++ b/bot/bot.py
@@ -1,6 +1,7 @@
 import asyncio
 import logging
 import socket
+import warnings
 from typing import Optional
 
 import aiohttp
@@ -17,20 +18,20 @@ class Bot(commands.Bot):
     """A subclass of `discord.ext.commands.Bot` with an aiohttp session and an API client."""
 
     def __init__(self, *args, **kwargs):
-        # Use asyncio for DNS resolution instead of threads so threads aren't spammed.
-        # Use AF_INET as its socket family to prevent HTTPS related problems both locally
-        # and in production.
-        self._connector = aiohttp.TCPConnector(
-            resolver=aiohttp.AsyncResolver(),
-            family=socket.AF_INET,
-        )
+        if "connector" in kwargs:
+            warnings.warn(
+                "If login() is called (or the bot is started), the connector will be overwritten "
+                "with an internal one"
+            )
 
-        super().__init__(*args, connector=self._connector, **kwargs)
-
-        self._guild_available = asyncio.Event()
+        super().__init__(*args, **kwargs)
 
         self.http_session: Optional[aiohttp.ClientSession] = None
-        self.api_client = api.APIClient(loop=self.loop, connector=self._connector)
+        self.api_client = api.APIClient(loop=self.loop)
+
+        self._connector = None
+        self._resolver = None
+        self._guild_available = asyncio.Event()
 
     def add_cog(self, cog: commands.Cog) -> None:
         """Adds a "cog" to the bot and logs the operation."""
@@ -38,22 +39,67 @@ class Bot(commands.Bot):
         log.info(f"Cog loaded: {cog.qualified_name}")
 
     def clear(self) -> None:
-        """Clears the internal state of the bot and resets the API client."""
+        """
+        Clears the internal state of the bot and recreates the connector and sessions.
+
+        Will cause a DeprecationWarning if called outside a coroutine.
+        """
+        # Because discord.py recreates the HTTPClient session, may as well follow suit and recreate
+        # our own stuff here too.
+        self._recreate()
         super().clear()
-        self.api_client.recreate()
 
     async def close(self) -> None:
-        """Close the aiohttp session after closing the Discord connection."""
+        """Close the Discord connection and the aiohttp session, connector, and resolver."""
         await super().close()
 
-        await self.http_session.close()
         await self.api_client.close()
 
-    async def start(self, *args, **kwargs) -> None:
-        """Open an aiohttp session before logging in and connecting to Discord."""
-        self.http_session = aiohttp.ClientSession(connector=self._connector)
+        if self.http_session:
+            await self.http_session.close()
+
+        if self._connector:
+            await self._connector.close()
 
-        await super().start(*args, **kwargs)
+        if self._resolver:
+            await self._resolver.close()
+
+    async def login(self, *args, **kwargs) -> None:
+        """Re-create the connector and set up sessions before logging into Discord."""
+        self._recreate()
+        await super().login(*args, **kwargs)
+
+    def _recreate(self) -> None:
+        """Re-create the connector, aiohttp session, and the APIClient."""
+        # Use asyncio for DNS resolution instead of threads so threads aren't spammed.
+        # Doesn't seem to have any state with regards to being closed, so no need to worry?
+        self._resolver = aiohttp.AsyncResolver()
+
+        # Its __del__ does send a warning but it doesn't always show up for some reason.
+        if self._connector and not self._connector._closed:
+            log.warning(
+                "The previous connector was not closed; it will remain open and be overwritten"
+            )
+
+        # Use AF_INET as its socket family to prevent HTTPS related problems both locally
+        # and in production.
+        self._connector = aiohttp.TCPConnector(
+            resolver=self._resolver,
+            family=socket.AF_INET,
+        )
+
+        # Client.login() will call HTTPClient.static_login() which will create a session using
+        # this connector attribute.
+        self.http.connector = self._connector
+
+        # Its __del__ does send a warning but it doesn't always show up for some reason.
+        if self.http_session and not self.http_session.closed:
+            log.warning(
+                "The previous session was not closed; it will remain open and be overwritten"
+            )
+
+        self.http_session = aiohttp.ClientSession(connector=self._connector)
+        self.api_client.recreate(force=True, connector=self._connector)
 
     async def on_guild_available(self, guild: discord.Guild) -> None:
         """
['bot/api.py', 'bot/bot.py']