Step 1: Prepare the Pan
Preheat the oven to 375°F. Lightly coat a 9×13-inch baking dish with nonstick spray. Line with parchment paper, allowing extra to hang over the sides, then spray the parchment as well.
Step 2: Make the Batter
In a large mixing bowl, beat together the sugar, sour cream, and softened butter until creamy. Mix in the mashed bananas and vanilla extract. In a separate bowl, whisk together the flour, baking soda, and salt. Slowly add the dry ingredients to the wet mixture, mixing just until combined. Gently fold in the chopped pecans.
Step 3: Bake and Cool
Spread the batter evenly into the prepared pan. Bake for 20–30 minutes, or until a toothpick inserted in the center comes out clean. Remove from the oven and allow the brownies to cool completely before adding the frosting.
Step 4: Brown the Butter
Cut the butter into pieces and place them in a heavy-bottomed skillet over medium heat. Stir often as the butter melts, foams, and begins to brown. When golden brown flecks appear and a nutty aroma develops, immediately transfer the butter to a heat-safe bowl to prevent burning.
Step 5: Prepare the Frosting
Gradually stir the powdered sugar into the browned butter, adding about one cup at a time. Pour in the milk and vanilla, then beat with an electric mixer until the frosting is smooth and easy to spread.
Step 6: Frost and Cut
Evenly spread the frosting over the cooled brownies. Once the frosting sets, use the parchment overhang to lift the brownies from the pan and slice into bars.