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, banana and egg to food processor.
Mix until dough looks uniform. *If dough seems a bit dry, add a tablespoon or two of water and blend until desired consistency.
Turn the dough out onto the countertop.
If the dough is too sticky to work with - sprinkle the countertop with a tablespoon or two of flour, and work some of the flour from the counter into the dough until it is no longer sticky.
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.