Preheat oven to 350°F.
Make the cake batter: In a large mixing bowl, combine the softened butter, applesauce, eggs, white sugar, and vanilla extract. Mix until smooth. Add the almond flour, oat flour, baking powder, and salt. Stir until fully combined and smooth.
Make the cinnamon sugar filling: In a small bowl, stir together the melted butter, oat flour, white sugar, and cinnamon until evenly combined. If it hardens, microwave for a few seconds.
Make the crumble topping: In a bowl, combine the room temperature butter, brown sugar, almond flour, oat flour, and cinnamon. Use your hands or a fork to mix until crumbly clumps form. Set aside.
Grease an 8x8 baking dish and line with parchment paper.
Pour half the cake batter into the dish and spread evenly. Spoon half the cinnamon sugar filling over the top and swirl into the batter using a knife or toothpick.
Add the remaining cake batter and spread evenly. Spoon the remaining cinnamon sugar filling on top and swirl again.
Bake for 25 minutes.
Remove from oven. Gently place the crumble topping evenly over the cake and press in lightly, especially in the center. Return to the oven and bake for another 18 minutes.
Remove from the oven and allow to cool completely before slicing into squares. Do not cut while warm - the cake needs time to fully set.