Preheat the oven to 350 degrees. In a mixing bowl, combine the eggs, banana and pumpkin puree, blending until smooth at medium speed with an electric mixer. Reduce the mixer speed to low and add the flour. Mix until completely incorporated.
Dust a rolling pin and clean surface with extra flour and transfer the dough. Roll out from ⅛-inch to no more than ¼-inch thickness and cut into cookies. Place on an ungreased baking sheet and bake for 20 minutes. Transfer to a wire rack to cool completely before treating your pet. These can be frozen for longer storage.
Recipe by The Tennessee Magazine at https://www.tnmagazine.org/cooking-for-the-dog-days-of-summer/