Preheat oven to 350°F and butter and flour a 9x5-inch loaf pan. Brown the butter in a saucepan over medium heat, swirling often, until amber and nutty, about 5-7 minutes. Cool until warm.

Whisk together browned butter, sugar, mashed bananas, eggs, sour cream, and vanilla until smooth.

In a separate bowl, combine flour, baking powder, baking soda, and salt. Fold the dry ingredients into the wet mixture just until no streaks remain.

Pour batter into the prepared pan and smooth the top. Bake 60-70 minutes until a toothpick inserted in the center comes out with moist crumbs. Cool in pan 10 minutes, then turn out onto a rack to cool completely.

Once fully cool, slice and serve with powdered sugar or salted butter.