I like to speedily do MC first (maybe using 1/3 or 1/2 of the allotted time for them), then essay fully, then go slowly through MC reviewing what I did and answering questions that I didn't do.
Honestly, if you need to jog your memory about the subject by doing MC first, you are probably unprepared for that exam.
I do it my way because I easily pick off the MC questions that I absolutely know and have no tricks to them/the short ones, so I KNOW I have some points. Then essays. If the essays are pretty simplistic, I will have plenty of time for MC. Worst case scenario, if the essay is on something I'm unprepared for, I have time to think out the response better. Then if time is coming close to running out, I know I have many points on the MC, and can just guess "D" or something on all the remaining MC questions (again, worst case scenario) and know I'm getting at least a few points.
You can't do that with essay questions, you have to write something to get points. With MC you could presumably get points by random guessing.