Preheat your oven to 350°F (175°C) and prepare an 8-inch square baking pan by greasing it with butter and lining the bottom with parchment paper.

In a medium saucepan, melt the unsalted butter over medium heat, cooking for 5-7 minutes until golden brown and nutty. Set aside to cool slightly.

In a large mixing bowl, combine the cooled brown butter with brown sugar and vanilla extract. Stir well before adding eggs, ripe bananas, sourdough discard, and buttermilk, whisking until smooth.

In a separate bowl, sift together all-purpose flour, baking soda, baking powder, and salt. Gradually fold the dry ingredients into the wet batter until just combined.

Pour the batter into the prepared pan and bake for 25-30 minutes, until a toothpick inserted into the center comes out clean.

Cool the cake in the pan for 20 minutes before transferring it to a wire rack to cool completely.

In a large bowl, beat together softened cream cheese and unsalted butter until fluffy. Gradually add powdered sugar, maple syrup, vanilla extract, ground cinnamon, and a pinch of salt until smooth.

Spread the cinnamon maple cream cheese frosting over the cooled cake, optionally drizzling extra maple syrup for added flavor.