Preheat an oven to 325 F. Grease and line a light-colored metal 8x8 baking pan with parchment paper so that you have some overhang over the sides of the pan.
Brown the butter. Add the butter to a small saucepan. Cook, swirling the butter occasionally, until golden brown with a nutty aroma. Pour the brown butter into a heat-safe mixing bowl and cool for 10 minutes.
Make the crumble topping. In a small bowl, combine the flour, brown sugar, walnuts, and salt and mix with a fork. Pour in the melted butter and mix until clumpy. Transfer to the fridge to firm up.
Mix the cinnamon sugar. In a small bowl, whisk together the brown sugar and cinnamon until well mixed. Set aside.
Mix the dry ingredients for the cake. Combine the flour, baking soda, and salt in a small bowl and whisk until combined. Set aside.
Mix the wet ingredients for the cake. Add the brown and white sugar to the slightly cooled brown butter. Whisk well for 2-3 minutes until thick and foamy. Whisk in the egg, sour cream, vanilla, and mashed banana until very smooth. Switch to a rubber spatula and fold in the dry ingredients until just combined and no streaks of flour remain.
Layer and bake. Spread half of the cake batter in the prepared baking pan in an even layer. Sprinkle the cinnamon sugar all over, then top with the remaining batter. Remove the crumble from the fridge and use a fork to break up the crumble into small pieces and sprinkle all over the top of the cake. Transfer to the oven and bake for 45-50 minutes, until slightly puffed in the center and a cake tester comes out clean. Remove from the oven and cool for 45 minutes.
Mix the glaze. Whisk together the powdered sugar, milk, and maple syrup until thick but drizzle-able. Drizzle the glaze over the cooled cake before cutting and serving.