In a large bowl, mix together the pumpkin puree, peanut butter, and eggs until well combined. Add most of the flour (keep ½ cup in the bowl - add up to ¼ cup more as needed, reserve ¼ cup for flouring during rolling.) Add the oats and stir until combined. The mixture will be stiff.
Flour your countertop or a board. Dump out the mixture, and knead a couple of times to make a ball. Flour your rolling pin and roll out the dough to desired depth – between ¼ inch and ½ inch. Thinner treats will allow you to make more with one batch and will bake faster. Thicker treats take longer to bake and make less. This is totally up to you!
Cut out shapes with a cooking cutter or biscuit cutter or cut into squares with a knife. Transfer shapes to a lined baking tray.
Gather up the scraps and re-roll until you have used all of the mixture.
Bake at 350F/176C for 25 minutes for thinner treats and up to 40 minutes for thicker treats. Remove from the oven and allow to cool on the baking sheet. They will crisp slightly as they cool.
Store in an airtight container at room temperature for up to 3 days, in an airtight container in the refrigerator for up to a week, or in the freezer for up to 2 months.