Preheat the oven to 350ºF and lightly grease an 8-inch square baking pan. Press a piece of parchment paper into the bottom of the pan for easier clean up. (Tip: A metal pan will give you better baking results than a glass or ceramic pan.)
In a large bowl, combine the oat flour, baking powder, cinnamon, and salt. Whisk well to break up any clumps. Add in the applesauce, eggs, maple syrup, avocado oil, and vanilla extract. Whisk again until smooth.
Pour the batter into the prepared pan. Sprinkle chopped walnuts over the top, if you like. (Chopped apple would also be nice!) Bake at 350ºF for 30 minutes, or until the center feels firm to the touch.
Let the cake cool in the pan for at least 30 minutes. Then slice it into 16 squares and serve. Top with cream cheese frosting, if desired. (Recipe in notes) Leftover cake can be stored in an airtight container in the fridge for up to a week. The top of the cake may become sticky if you leave it out at room temperature for a while. (This is normal!)
Notes
Nutrition information is for 1 of 16 slices without the optional topping. This information is automatically calculated and is just an estimate, not a guarantee.Gluten-Free Note: Oats are naturally gluten-free but they can be contaminated during processing. Buy a package that says "certified gluten free" if needed. To make your own oat flour, blend rolled oats in a dry blender until they have a flourlike texture. (You could also blend the batter in the blender!)Cream Cheese Frosting: Make a healthier cream cheese frosting by combining 4 ounces of softened cream cheese, 3 tablespoons of greek yogurt, and 2 tablespoons of honey. You can also add a 1/4 teaspoon of vanilla extract, if you like. Mix with an electric