Preheat oven to 350°F (176°C). Line baking sheet with parchment paper or silpat, set aside.
Add oats to the bowl of a food processor.
Let machine run for 2 - 3 minutes, until oats are almost flour consistency with a few big pieces left.
Add peanut butter, pumpkin purée and egg to food processor.
Mix until dough looks uniform.
Turn the dough out onto the countertop.
Dough will be sticky - sprinkle the countertop with a couple of tablespoons of flour, and work some of the flour from the counter into the dough until it is no longer too sticky to roll out.
Roll the dough out to roughly 1/8" thick.
Cut treats out with cookie cutter and place on baking sheet. Bake for 16 - 18 minutes, rotate trays halfway through.
Cool completely before giving to your dog.