Preheat the oven to 350°F. Grease an 8-inch square cake pan and line it with a piece of parchment paper that extends up and over two opposite sides of the pan.
In a large bowl, whisk together the ½ cup unsalted butter, ⅔ cup light brown sugar, 2 teaspoons pure vanilla extract, 2 large eggs, ¼ cup plain yogurt, and 1 cup mashed bananas until smooth. Whisk in the 1 teaspoon baking soda and ½ teaspoon fine salt, then fold in the 1 ½ cups oat flour and ¼ cup almond flour until just combined.
Scrape the batter into the prepared pan and smooth the top. Sprinkle the ½ cup mini chocolate chips evenly over the top. Rest the batter while the oven heats.
Place in the oven and bake for 30-35 minutes, until a tester comes out clean. Cool on a wire rack for 30 minutes, then either cut and serve from the pan or transfer the cake to a plate to serve.
Notes
Use ripe bananas. The riper the bananas, the sweeter they will be and the easier they will blend into the batter. You can even try to reduce the amount of sugar by ¼ cup if your bananas are very sweet.
Brown the butter. For a fabulous extra note of flavor, brown the butter. Cook it over medium heat until slightly nutty-smelling and browned. Make sure to cool a bit before using.
Egg-free: This cake takes well to being egg-free because bananas already have a fantastic binding ability. Add 1 flax egg instead of the eggs: mix 1 tablespoon ground flaxmeal in 3 tablespoons of water, let sit for 5 minutes, then add to the batter.
Flour options: Any whole grain gluten-free flour is great here. I of course love oat flour, but sorghum or brown rice flour also works well. If you don't need to eat gluten-free, use a whole grain flour like spelt flour or whole wheat or whole wheat pastry flour. All-purpose flour may also be used.
Dairy-free: Use dairy-free butter or melted coconut oil for the butter, and use dairy-free yogurt or non-dairy milk for the yogurt.
Add a little spice. Warm up the cake with 1 teaspoon of ground cinnamon or ½ teaspoon cinnamon + ½ teaspoon ginger.