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.): You'll smell the faint warmth as the oven comes up to temperature, which helps develop an even bake and a golden top. Proper pan preparation prevents sticking, and parchment gives you a clean release and tidy slices afterward. Using a metal pan encourages crisper edges and a shorter bake time than glass, which stays cooler; watch for a gently domed, lightly browned top. A common mistake is skipping the parchment, which can cause the cake to tear when removed, so take the extra minute to line the pan carefully and lightly grease the sides so the parchment adheres.
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.: As you whisk the dry ingredients you will notice the flour becoming aerated and the batter smells faintly of spice, which is a good sign of even distribution. Adding the wet ingredients and whisking until smooth creates a glossy, unified batter with no streaks of flour. This blending step matters because it ensures even rise and consistent texture; pockets of powder can create dry spots. A common error is over mixing after adding wet ingredients, which can tighten the texture, so whisk just until uniform and stop when the batter looks smooth and slightly thickened.
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.: Pouring the batter in reveals a batter that is thick but pourable, and you should spread it gently to the corners for even thickness. The walnuts give a visual cue and aroma as they toast; you will hear tiny crackles as they warm. During baking the kitchen will fill with the scent of cinnamon and maple, and the surface should become light golden. The center feeling firm to the touch indicates set crumb, while a wobbly center means it needs more time. Avoid opening the oven repeatedly, as that can drop the temperature and lead to uneven baking.
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!): Cooling is where the cake finishes setting, and the residual heat evens out the crumb. After 30 minutes the edges will slightly pull away from the pan, and the surface will have a matte finish rather than shiny. This resting time helps produce clean slices, so resist slicing while it is still warm, which can lead to a gummy texture and crumbly pieces. A common oversight is impatiently cutting too early, which makes the cake fall apart, so plan to let it rest for the recommended time.
Then slice it into 16 squares and serve. Top with cream cheese frosting, if desired.: When you slice the cake into 16 squares you should feel a slight resistance as the knife passes through the tender crumb, leaving neat edges if cooled properly. Serving it plain showcases the gentle spice and apple notes, while a light cream cheese frosting adds tang and creaminess. If you choose frosting, allow the cake to cool completely, otherwise the frosting can melt and slide. A trap to avoid is adding frosting too soon, which will make it run and create an overly sweet finish rather than a balanced one.
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.: Stored chilled, the cake retains moisture and the flavors meld for even tastier slices over the following days, though refrigeration can slightly firm the crumb. If you prefer softer slices, bring squares to room temperature before serving, which revives the mouthfeel. Leaving the cake uncovered at room temperature can cause the top to become sticky from the maple and apple sugars; this is normal but can be mitigated by refrigeration. A common mistake is leaving it on the counter uncovered overnight, which can accelerate stickiness and attract humidity, so use an airtight container for best results.