Preheat the oven to 350°F (180°C) and line a baking sheet with parchment paper.
In a large mixing bowl, mash the ripe banana until smooth.
Add the peanut butter and mix until well combined.
Gradually add the rolled oats, stirring until evenly distributed.
Add water and mix until the dough comes together. If the dough is too dry, add a little more water, one tablespoon at a time.
On a clean surface or silicone baking mat, roll out the dough to approximately 1/4-inch thickness.
Use your favorite cookie cutter shapes (such as bones or hearts) to cut out treats from the dough. Alternatively, you can simply cut the dough into small squares.
Place the treats onto the prepared baking sheet, leaving some space between each treat.
Bake for 25-30 minutes, or until the treats are golden brown and firm to the touch.
Remove from the oven and let the treats cool completely on a wire rack.