Preheat oven to 325°F (163°C). Line two large baking sheets with parchment paper or silicone baking mats. Set aside.
In a large bowl, gently mix the peanut butter, milk, egg, and carrot together with a wooden spoon or rubber spatula. Add the flour and baking powder. You may need to turn the dough out onto a floured work surface and use your hands to work in the flour. Mix in the oats. The dough is extremely thick and heavy.
Using a floured rolling pin, roll the dough out into 1/4" thickness. Cut into shapes using cookie cutters. Arrange on the baking sheets. Bake for 15 minutes, or until very lightly browned on the bottom. Remove from the oven, and flip the treats to bake the other side for 10 more minutes. Want the treats to be a little more crunchy? Bake for 5 more minutes.
Allow to cool completely before serving to your pup. Store at room temperature or in the refrigerator for up to 1 week.
Make ahead/freezing: Since the pups can't eat the whole batch in a week, I usually freeze them. Jude loves them right out of the freezer too! The treats freeze well up to 2 months.
Unbleached all-purpose flour is safe for dogs, but whole wheat was more highly recommended by our vet because of its added health benefits. Again, please consult with your vet about any allergies your dog may have.