Preheat the oven to 350°F and line a baking sheet with parchment paper.

In a medium mixing bowl, mash the ripe banana until mostly smooth.

Add the peanut butter and egg to the bowl and stir until the mixture is creamy and well combined.

Gradually add the oat flour to the wet mixture, stirring until a soft, non-sticky dough forms that holds its shape when pressed.

Lightly dust a clean work surface with a small amount of oat flour and place the dough on it.

Roll the dough out to about 1/4 inch thick using a rolling pin.

Use small cookie cutters to cut shapes from the dough and place them on the prepared baking sheet.

Gather any dough scraps, reroll, and cut additional treats until all the dough is used.

Bake the treats for 18 to 20 minutes, or until the edges are lightly golden and the centers feel firm to the touch.

Remove the baking sheet from the oven and let the treats cool completely on the sheet before serving or storing.