First speech bubble. It’s correct!
That “whom” sounds wrong because we’re used to hearing the subject of the sentence first. That ‘whom’ is really the object of “of.” You can also say that the “whom” is introducing the noun clause that’s the direct object of “know”!
To fix the word order a bit, you’d have:
Do you know of whom she reminds me?
Of course now you have a rather awkward question. I fear that “who” will become the only form to appear at the beginning of a sentence regardless of the word’s function in the sentence.
PS—If it were me, I’d write. “Hey! She reminds me of someone I knew.”
PPS—Since I ran into it today, here’s a strip that gets it wrong twice. Second panel:
PPPS—And here’s one where he gets it right. First panel.
This post first appeared on The Writing Rag.