Everything about his face, was circular, like most (of the) ingredients of a hamburger.
Do I need of the. Why or why not?
Well no, you are talking about most ingredients or most of the ingredients. It doesn't matter. I would put:
Everything about his face was circular, like most of the ingredients in a hamburger.
Note I have put in a
instead of of a
and removed the comma in face, was
to make the flow run smoother
No, you do not need "of the."
Without, you are discussing most of an unknown/non-specific set of ingredients in hamburgers generally.
With, you are discussing most of the specific ingredients in a hamburger.
If I recall correctly, we call these "unspecific" and "specific" groups.