If you try to give your dog broccoli for the first time and they like the way it tastes, they are going to eat it quickly and without any signs of hesitation. After that, your dog is likely to beg for more of the veggie by standing close to you and the food until you share more, paw at you, stare intently, wag their tail, look alert and focused on the food, and they will also drool and lick their lips a lot as well.