Q:

How do I get “restart” option in the system menu in Gnome Classic?

I previously asked a similar question about Unity, but now I'm using (and sticking with) Gnome Classic.
There is this drop down menu in the top right corner of the Gnome panel:

When you press "Shut down", you get a dialog window that comes up with the following options:

However, because I probably restart as much or more than shut down, and I never suspend or hibernate, I'd like to move the "Restart" from the dialog window to the drop down.
Is it possible to place a "restart" option right into the dropdown menu?

A:

This is not possible without rewriting the source code for GNOME Panel. The actions in the menu you're referring to are constructed from this list, which does not include a restart item and isn't extensible using configuration files.
If you're feeling ambitious and want to patch in a restart menu item for yourself, creating a panel_session_manager_request_restart analog of this function would be the place to start.

