Preheat the oven to 350 degrees F. Line an 8x8 inch pan with parchment paper and spray with nonstick cooking spray.
First make your streusel: 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 begins to form into crumbles and resembles clumps of wet sand. You may need to use your hands/fingers to form into nice thick ‘crumbs’. Cover the bowl with plastic wrap and place in the fridge until ready to use.
Make your brown butter: add ⅓ cup butter to a large saucepan or skillet and place over medium heat. The butter will begin to melt, crackle, and then eventually foam. Make sure you stir constantly during this process. After a couple of minutes, the butter will begin to brown and turn a nice golden amber color on the bottom of the saucepan, this usually happens right when it foams. Continue to whisk and remove from heat as soon as the butter begins to brown and give off a nutty aroma. Set aside to cool for 5-10 minutes.
In a large bowl, mix together the wet ingredients until well combined: applesauce, eggs, maple syrup, vanilla extract and cooled brown butter.
In a separate medium bowl: whisk together the flour, baking powder, baking soda, cinnamon, allspice, ginger, nutmeg and salt. Add the dry ingredients to the wet ingredients and mix until just combined; do not overmix. Fold in the chopped apples.
Pour HALF of the batter into the prepared pan; sprinkle with HALF of the streusel mixture. Then top with half of the remaining batter and top with remaining streusel mixture.
Bake for 40-50 minutes or until a tester comes out clean with just a few crumbs attached. Allow the cake to cool for 30 minutes before glazing.
To make the glaze: In a small bowl, mix together the melted butter, powdered sugar, vanilla, cinnamon and milk. Start with a little bit of milk to thin the glaze, knowing you can always add more to thin if necessary. Drizzle the glaze back and forth over the cake. It does make a good amount of glaze, so you can always cut it in half or omit it from the recipe (but I highly recommend the drizzle!). Cut into 12 slices. Store covered at room temp for 1-2 days, then transfer to the fridge for up to 1 week.