I could not find the original thread, and I am not sure if
this one refers to mine, which would be an honor.
You must know that Rich Turner was the original "mudge" or curmudgeon and legend has it that he could go months or longer without being caught in a grammatical error, although typos seemed to be his friend. When others on the board caught him in an error, they were lauded for days. CeeBee, on the other hand, is my go to grammar person, and I trust her implicitly.
This exchange shows that while the possessive pronoun is usually the correct pronoun to use, the non-possessive pronoun can be correct. It depends if you are referring to the subject of the phrase, "you cooking" or to the gerund itself in which case it would be the more common "your cooking."
The mudge above clearly falls back on the trap of what sounds correct, or something one would not do as in "I appreciate you." As a matter of fact, one would say this and, using that as part of his argument, was his downfall. Not the typical Mudge. But, as his passed away two months later that could explain it.
The sentence that I believe Garonsky used to prove his point to me was something like the following from The Beverly Hillbillies:
I am going to watch Jane Hathaway's playing tennis today, but I would much prefer to watch Elly Mae Clampett playing tennis.
Apologies in advance for the chauvanism.
