1-Preparing the Banana Bread Bars: First, preheat your oven to 350°F (175°C) and grease an 11×15 inch jelly roll pan to prevent sticking. Next, brown the unsalted butter over medium heat until it turns a light amber color, using about 1 1/4 cups total for both the bars and frosting, minus the 2 tbsp chilled butter.

2-Preparing the Banana Bread Bars: Divide the browned butter by reserving 1/2 cup for the bars, and pour the rest into a bowl with the 2 tbsp chilled butter, then refrigerate it for the frosting. In a separate bowl, whisk the reserved 1/2 cup browned butter with the granulated sugar and packed light brown sugar until well mixed.

3-Preparing the Banana Bread Bars: Add the eggs, followed by the sour cream, mashed bananas, and vanilla extract, stirring everything together thoroughly. Stir in the baking soda and salt, then fold in the all-purpose flour just until combined to keep the bars tender; avoid overmixing as that can make them tough.

4-Preparing the Banana Bread Bars: Pour the batter into your prepared pan and spread it evenly for uniform baking. Bake for 25-30 minutes, checking with a toothpick to ensure it comes out clean.

5-Creating the Brown Butter Frosting: Once the refrigerated brown butter mixture is solid but soft, beat it with a mixer using a whisk attachment. Gradually add the powdered sugar, one cup at a time, until it’s fully incorporated for a smooth consistency.

6-Creating the Brown Butter Frosting: Beat in the vanilla extract and room temperature milk until the frosting is creamy and spreadable. Spread it over the slightly warm bars, then let everything cool for about 30 minutes before slicing.