Place rack in center of oven. Preheat to 350 F degrees. Line the bottom of a loaf pan, grease the sides. Set aside.
In a food processor, add the bananas and puree until smooth. Add brown sugar, granulated sugar, vanilla, and eggs until frothy.
With the processor running, add oil in a steady stream. Process an additional 30 seconds until emulsified.
Add the oat flour, baking powder, baking soda, cinnamon, nutmeg, and salt. Pulse to combine.
Pour batter into prepared baking pan. Smooth out top. Bake 35 to 40 minutes, until a toothpick comes out clean.
Place cake on wire rack and allow to cool for 10 to 15 minutes. Loosen the edges with a knife and turn out onto rack. Cool completely (if you can wait that long!).
Notes
This recipe is gluten-free only if certified gluten-free oat flour or gluten-free certified oats are used.