Preheat oven to 325°F (160°C). Lightly grease two 4-inch round pans, or a small 6-8 inch pan, or 4 - 6 muffin cups.
In a medium bowl, whisk together the oat flour and baking powder. Add the mashed banana, peanut butter, and 4 tablespoons of water or plant milk. Mix into a very thick, sticky batter. If needed, add 1 more tablespoon of liquid to help it come together, but not more than that.
Spread the batter evenly into your prepared pan(s). The batter will be thick and sticky, so you can optionally wet your spatula or fingers to help smooth the top.
Bake for 30–35 minutes, or until the edges are lightly golden and a toothpick inserted comes out clean. Let the cake cool fully before frosting.
In a small bowl, mix the peanut butter and yogurt until smooth. Add a water or plant milk one teaspoon at a time if needed to thin.
If making layers, spread frosting between layers and over the top. Add berries, banana slices, carrot, or dog treats if desired.
