Since the ice cream is added, I think of this more like a dessert. However - if you're unable to have caffeine later in the day, eat it earlier! Part of the perks of being an adult is that you can have your ice cream, and enjoy it. If you want to have a coffee milkshake for breakfast, make it happen. This could also be a super fun addition to brunch or even a lunch option. And if you do want to enjoy it for dessert at night, just swap out the caffeine and use decaf instead. You won't even notice a difference in the flavor or taste.