One of my two dogs got into the cookie jar — do I need to monitor the other dog who didn't eat any?

No, you only need to focus on the dog that ate the cookies. Cookies pose a mild risk because they often contain harmful ingredients like chocolate chips, raisins, or the sweetener xylitol, which is highly toxic. Check what type of cookies were eaten, as that determines the next step. For the dog that didn't eat any, there's no action needed. For the one that did, watch closely for vomiting, lethargy, or tremors, and call your vet promptly if you see any of those signs.