Hi, my name is XXXXX XXXXX i'm happy to offer you some help today.
The problem you described sounds very similar to something ive seen often, hopefully i can help.
If it hasn't been checked already, have the dealer (or your mechanic) take a look at the intermediate steering shaft. It connects the lower steering column to the steering rack. there are several service bulletins involving noise from these, and ive replaced many.
Can you feel anything in the brake pedal when it makes this noise?
I see. Well thats definately different then what i had in mind. I don't believe i have come across this particular issue.
I'll opt out, and we'll open this question to other gm experts to respond to see if someone else has ok?
Good luck, im sure one of the other experts will have something for you shortly. thanks.