I would like it so that if I'm searching for something in Controlling that I can hit the Esc key on my keyboard as a shortcut for clicking on "Done" or unfocusing that search box. I don't care which one. I just don't like using the mouse when I don't have to.

Would pressing esc to unfocus the text box work? that way you would have to press it twice to back out of the menu.

Yes, the more I think about it, pressing Esc to unfocus the text box would be the preferable way. I've gotten into the habit of pressing Esc after searching in JEI to unfocus that search field.