Can I remind a professor that I submitted a "good" essay in her class? (LOR request) I would like to ask my former professor for a reference, I'm not sure how to formulate it and am worried the professor won't remember me. I submitted a good essay in her class though (got an A).

Can I write:


  Dear Professor, 
  
  I studied with you 2 years ago, I don't know if you
  remember. In any case, I submitted a good essay in your class and
  wanted to ask you for a letter of recommendation?
A better outline might be somehting like:


  Dear Professor Smith,
  
  I am planning to apply to Teleportation programme at the University of
  Wonderland for my graduate studies. They require two reference
  letters, and your area of interest is related to the programme I am
  applying to.
  
  Would you please be kind enough to write a letter of recommendation?
  
  I have taken your course Introduction to Supernatural Incidents (ISI
  101) in 2016 - 2017 Fall semester, and you have noted that one of my
  assignments were outstanding.


Keep in mind that if you suspect that the professor wouldn't even remember you, it is better not to ask that professor for a letter of recommendation, because chances are they are going to write a mediocre letter.

Why did I pick this outline

Because first of all, the reason for you writing a mail should be explained at the first sentence. An avarage professor mailbox receives around 100 mails per day. Thus, they decide whether or not to read the full mail in a few seconds.

The actual reason for such mail is your application for graduate studies, and you give solid reasons for the letter of recommendation. Note that in your outline, the letter of recommendation is just mentioned. It seems like you wanted to remind the professor that you were his student, and handed in a good essay.

Another reason is, the punctiation and language. Although overly-formal emails are not good, using a proper language helps.

To sum up, the professor wants to know three things very clearly, and as soon as possible:


Why are you writing this mail?  
What do you want from me?
Why would I grant your wish?