Instructions

• Preheat oven to 375F. Grease and flour a 9×13-inch pan.
• In a large bowl, beat together 1½ cups sugar, 1 cup sour cream, ½ cup softened butter, and 2 eggs until creamy and well combined (about 1–2 minutes with an electric mixer or vigorously by hand).
• Stir in 3–4 ripe mashed bananas (about 2 cups) and 2 teaspoons vanilla extract until evenly distributed.
• Add 2 cups all-purpose flour, 1 teaspoon baking soda, and ¾ teaspoon salt. Mix on low speed or stir until just combined, about 30–60 seconds. If using, fold in ½ cup chopped walnuts.
• Spread the batter evenly into the prepared 9×13-inch pan using a spatula.
• Bake in the preheated oven for 20–25 minutes, or until the top is golden brown and a toothpick inserted into the center comes out with only a few moist crumbs.
• Remove the pan from the oven and let the bars cool in the pan for about 5 minutes so they are warm but not piping hot.
• While the bars are cooling, make the brown-butter frosting: in a medium saucepan over medium heat, melt ½ cup butter. Continue cooking, stirring or swirling occasionally, until the butter foams and turns a light golden brown and smells nutty. Remove from heat immediately.
• To the browned butter, add 4 cups powdered sugar, 1½ teaspoons vanilla extract, and 3 tablespoons milk. Whisk until smooth; the mixture should be thicker than a glaze but thinner than a typical frosting.
• Use a spatula to spread the brown-butter frosting over the warm bars in the pan. Let the frosting set at room temperature, then cut into bars and serve.