Preheat oven to 350 degrees. Line a baking sheet with parchment paper.
Place pumpkin puree, eggs and peanut butter in the bowl of a stand mixer fitted with paddle attachment. Mix on medium for 1 -2 minutes. Turn mixer down to low and add in whole wheat flour slowly. Turn mixer up to medium and mix until dough resembles small balls. If mixture looks too dry add a little water and if it looks too wet add a little more whole wheat flour.
Gather dough into a ball and turn out on a lightly floured work surface. Roll dough to about 1/4 inch thickness. Cut out shapes and place on parchment lined baking sheet. They do not expand so you do not have to place them far apart. Bake 15-20 minutes if your dog likes softer treats and 30 minutes if they like harder, crunchy treats. (I used a medium sized fire hydrant cookie cutter from Williams-Sonoma and I made about 30 treats.) Let cool on tray.
These treats will last a few days out on your counter. You can also refrigerate them and they will last about a week.