Preheat oven to 350 degrees F
Place oatmeal into a blender or Cuisinart and blitz for several seconds until it is more of a flour-like texture. Reserve a couple tablespoons for rolling out the dough.
In a medium bowl stir together remaining oats, mashed banana and peanut butter until thoroughly mixed together. If you find the dough is dry and crumbly add a bit more peanut butter until it becomes more pliable. Alternatively, if you have a really wet dough, you may need to add in the reserved oat flour to achieve that pliable texture. Using your hands, gather dough together into a ball.
Transfer dough to countertop sprinkled with some of the reserved oat flour or other gluten free flour. Using your hands, first shape the ball into a disk shape, and then gently roll out dough to a thickness of about 1/4" using additional oat flour or other gluten free flour to keep the dough from becoming sticky. Cut dough into desired shapes and gently transfer to lined (either with a silicone mat or parchment paper) cookie sheet. Alternatively, if you don't want to roll out your treats, scoop dough into approximately tablespoon portions, roll into balls and then flatten with the palm of your hand onto the cookie sheet.
Bake for about 15 minutes or until edges just start to darken. Allow to cool 15 minutes or so before sharing with your furry friend, or trying yourself! This recipe should yield about 18 treats (3 1/2' x 1 1/2").