Preheat oven to 350°F (175°C).
Grind oats in a blender or food processor until they form a soft flour-like texture (about 20–30 seconds).
In a medium bowl, mix peanut butter and egg until smooth and combined.
Gradually add oat flour to the peanut butter mixture, stirring until crumbly. Add warm water a little at a time until a soft dough forms that holds together without being sticky.
Lightly dust a work surface with extra oat flour. Roll dough to about 1/4 inch thick.
Cut into shapes using a small cookie cutter or knife. Place on a parchment-lined baking sheet with space between treats.
Bake for 18–22 minutes, depending on thickness. Thinner treats will be crispier; thicker ones stay softer inside.
Cool completely on a rack before serving. Store in an airtight container at room temperature for up to 5 days, refrigerate for up to 2 weeks, or freeze for several months.