I pronounce it praw-cess.
What about “prah - cess”?
I say ‘prah [rhymes with bra]-cess’. I know several people who pronounce it pro-cess (as in a contraction of ‘pro-cedure for cess pools’).
No vote. PRAH-sees here as well. For me, it doesn’t rhyme with “bra” (which is more like “braw” in my dialect). It rhymes with the “ah” in “Say AHHHHH!”
You know, I read this thread title and thought, “There are only two ways I can think of to pronounce ‘process’ and none of these are it.” I think he means praw-cess to mean rhymes with bra-cess, and proh-cess to sound like pro-cedure. No? Because otherwise, my answer is neither one.
How about, for simplicity’s sake, the “praw-cess” response would also include “prah-cess”? I don’t really differentiate the -aw sound from the -ah sound, but now I realize some people do.
I pronounce it both ways depending on the sentence.
I pronounce the verb with a short O and the noun with a long one.
And you a Yankee, although my Paternal Grandmother hailed from your state.
I am surprised that we agree. 
You should have included, “Where are y’all from?” in your poll.
Depends what day it is.
prɑsɛs
The Director of my bit of the office is from somewhere in Yorkshire and always causes me to giggle when he says “prooooooooooooooo-cess” (as he does alarmingly often).
PRAH-cess, for all usages.
It seems like this one should be preceded with “Pick the closest answer to the one you use most frequently.” So I went with the top.
I generally pronounce it with the a in bra, which I would generally transliterate AH. I use AW for the longer, slightly rounded version. It’s the difference between Ah of recognition (Ah! I get it.) and the aw of empathy/cuteness (Aw, that’s cute/sad.)
PRO-cess
I find myself doing both, depending on the context.
Depends on who I am with. The Brits I know pronounce it with PRO, so when I’m with them that is how I do it. Most of the Yanks I know pronounce it the other way, so when I’m with them, that is what I do.
It almost comes out a bit like PRAS - ceyes.
But the accent is strong in me.
Otherwise - I probably sound more like NinetyWt and Sampiro.
A more contentious debate might be regarding the plural.
process-әz
vs.
process-eez
(first syllable pronounced to your liking but what about the last?)