If I melted 2 sticks of butter for a cookie recipe, then got diverted from making the cookies, how long will that butter keep? (I did not put it back in the fridge.)
Are you channeling your best self with this comment? (If you're not sure, check out our Code of Conduct.)
Hmmm… I can't remember ever being presented with this issue before. Trying to reason it through, I see a safety issue as the freed water collects with the milk solids. Water + protein = potential hazard. It would be a different situation under refrigeration. You could mitigate the hazard by making brown butter and then using that to make cookies. The high temp should kill any nasties and brown butter in cookies is a real treat.
Just cook it down to make ghee which has a looong shelf life