Preheat your oven to 350 degrees F. Line an 8x8 inch pan with parchment paper and spray it with nonstick cooking spray. This will ensure your cake comes out easily and stays moist.
Make the streusel first: In a medium bowl, mix together the flour, brown sugar, cinnamon, and salt. Add in the melted butter and stir together with a fork until it forms clumps resembling wet sand. You might need to use your hands to create nice thick crumbs. Once done, cover the bowl with plastic wrap and refrigerate until ready to use.
Next, let’s make the brown butter: Add ? cup of butter to a large saucepan or skillet set over medium heat. The butter will begin to melt and crackle, eventually foaming. Stir constantly. After a few minutes, it will brown and turn a lovely amber color, releasing a nutty aroma. Remove from heat and let it cool for 5 to 10 minutes.
In a large bowl, mix the applesauce, eggs, maple syrup, and cooled brown butter until well combined. This mixture will add moisture and depth of flavor to your cake.
In a separate medium bowl, whisk together the remaining flour, baking powder, baking soda, cinnamon, allspice, ginger, nutmeg, and salt. Add these dry ingredients to the wet ingredients and mix until just combined; be careful not to overmix. Finally, gently fold in the chopped apple.
To assemble the cake, pour half of the batter into the prepared pan. Sprinkle with half of the streusel mixture, then add half of the remaining batter on top, followed by the rest of the streusel. This layering will create a beautiful texture.
Bake for 40 to 50 minutes, or until a tester comes out clean with just a few crumbs attached. The cake should be golden brown and fragrant.
Once baked, allow the cake to cool in the pan for 30 minutes before glazing.
To prepare the glaze, in a small bowl, mix together the melted butter, powdered sugar, vanilla, cinnamon, and enough milk to reach your desired consistency. Drizzle the glaze back and forth over the cake. You can adjust the amount of milk for a thicker or thinner glaze.
Finally, cut the cake into 12 slices and enjoy! Store any leftovers covered at room temperature for 1 to 2 days, then transfer to the fridge for up to a week. This cake only gets better as the flavors meld together!
