Preheat oven to 350°F (175°C).

In a bowl, mix together pumpkin puree, egg, and rolled oats until well combined.

Pour batter into a greased or parchment-lined cake pan or muffin tin, spreading to about 1 inch thick.

Bake for 20-25 minutes until the top is firm and golden; a toothpick inserted in the center should come out clean.

Let the cake cool completely before slicing into dog-friendly portions and serving.