Preheat oven to 350 degrees F. Line a baking sheet with parchment paper or a silicone baking mat; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat pumpkin puree, peanut butter and eggs on medium-high until well combined, about 1-2 minutes. Gradually add 2 1/2 cups flour at low speed, beating just until incorporated. Add an additional 1/4 cup flour at a time just until the dough is no longer sticky.
Working on a lightly floured surface, knead the dough 3-4 times until it comes together. Using a rolling pin, roll the dough to 1/4-inch thickness. Using cookie cutters, cut out desired shapes and place onto the prepared baking sheet.
Place into oven and bake until the edges are golden brown, about 20-25 minutes.
Let cool completely.
Consult your pet's veterinarian regarding possible allergies your dog may have.