Place the butter in a medium saucepan over medium heat. Let it melt and continue cooking, swirling the pan occasionally until the butter turns golden brown and smells nutty (5-7 minutes). Be careful not to burn it.
Remove from heat, pour into a heatproof bowl, and let it cool slightly (5-10 minutes).
Preheat oven to 350℉ (180℃). Grease a 9x5-inch loaf pan with baking spray; set aside.
In a large bowl, whisk the mashed bananas, brown sugar, granulated sugar, eggs, vanilla extract, and sour cream.
Slowly whisk in the slightly cooled brown butter until well combined.
In another bowl, combine flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
Add the dry ingredients to the wet ingredients in 3 batches, gently folding until just combined, being careful not to overmix.
Pour mixture into the prepared loaf pan and top with sliced banana. Bake for 55-65 minutes, or until a toothpick inserted comes out clean.
Cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.