1. Preheat the oven to 350°F. Line a large shallow baking sheet with parchment paper.
2. Combine the flour and oats in a medium bowl. Whisk together the peanut butter, banana, egg, sugar and oil in a separate bowl. Pour the wet ingredients into the dry and stir with a spoon or rubber spatula until a rough dough forms. Knead the dough in the bowl 5-6 times until it comes together.
3. Turn the dough out onto a lightly floured work surface and roll to a 1/4-inch thickness. With a 1 3/4-inch bone shaped cookie cutter, cut out treats and transfer to the prepared baking sheet. Press all the scraps together, kneading once or twice, then roll out to 1/4-inch thickness and cut out more treats; repeat if necessary.
4. Bake treats until lightly browned and fairly hard, rotating the pans from top to bottom once, about 20-25 minutes. Remove from the oven and cool completely; biscuits will harden as they cool. Store in an airtight container.