Of course you can still bake it- the question is whether the cookies you make will be safe to eat. Honestly, nobody can really give you a good answer on that. Food safety experts will certainly tell you no, in big bold letters. The main threat would be salmonella contamination from the eggs, although there could be any number of other bacteria and virus involved in the mix. Those have many days to reproduce, and plenty of sugar to do it with. Most all are killed and inactivated by the baking process, although doing that will spread the contamination to other places, like your hands, utensils, and other surfaces where you can pick it up later. Though I'm as budget conscious as the next person and dislike food waste, I also am cautious with food safety. What you have there is a potential germ bomb, and I can only say I would not risk it.
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Also, if you postpone baking in the future, cookie dough stores safely in the freezer.