Preheat oven to 350 degrees F. Spray an 8″ square or 11 x 7″ baking pan with cooking spray and set aside.
In a large mixing bowl, mash banana until smooth. Add egg, milk, sugar, oil, applesauce, and vanilla, and whisk together very well. (You can also do this with an electric mixer if you prefer.)
Add flour, baking powder, and salt, and whisk vigorously for about a minute. (Again, use an electric mixer if you’d like. I apparently wanted an arm workout when I made this cake.)
Spread about half of cake batter in the prepared baking dish. Whisk cocoa powder into the remaining batter, and pour it on top of the plain batter. Use a spoon to swirl the two batters together, but don’t swirl too much or you’ll end up with chocolate cake instead of a marbled effect.
With a pastry cutter, fork, or your fingers, blend the butter, flour, and sugar together. Add cashews and chocolate chips, and mix a little more until they are evenly distributed. Crumble this butter mixture over the top of the marbled batter.
Bake in preheated oven for 40-45 minutes until edges are brown and toothpick inserted in center comes out mostly clean. Serve immediately or cooled.