Prepare the Baking Pan: Begin by preheating the oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper or lightly grease it with butter. This step ensures the brownies release easily once baked and keeps the edges from sticking.
Cream the Butter and Sugar: Place softened butter and granulated sugar into a large mixing bowl. Beat them together until the mixture becomes light and creamy. This process creates a smooth base that helps the brownies bake with a soft, even texture.
Add Eggs and Sour Cream: Crack the eggs into the bowl and mix until fully combined. Stir in the sour cream next. The sour cream adds moisture and richness, which helps the brownies stay tender and soft after baking.
Mix in Bananas and Vanilla: Mash ripe bananas in a separate bowl until smooth. Add the mashed bananas and vanilla extract to the batter, then stir gently until everything blends together. The batter should smell sweet and slightly fruity at this stage.
Combine the Dry Ingredients: In another bowl, whisk together flour, baking soda, and salt. Slowly add the dry mixture to the wet ingredients, stirring just until combined. Avoid overmixing so the bars remain soft instead of dense.
Spread the Batter in the Pan: Pour the banana batter into the prepared baking pan. Use a spatula to spread it evenly across the surface so the brownies bake at the same thickness throughout the pan.
Bake the Banana Brownies: Place the pan in the oven and bake for about 20 to 25 minutes. The surface should turn lightly golden, and a toothpick inserted in the center should come out mostly clean with a few moist crumbs.
Brown the Butter for Frosting: While the brownies cool slightly, melt butter in a saucepan over medium heat. Continue cooking until the butter turns golden brown and develops a nutty aroma. Stir occasionally and watch carefully so it does not burn.
Prepare the Frosting: Remove the browned butter from heat and whisk in powdered sugar, vanilla extract, and milk. Continue mixing until the frosting becomes smooth and pourable. The texture should resemble a thick glaze.
Frost the Warm Brownies: Spread the brown butter frosting over the slightly warm banana brownies. The warmth helps the frosting glide across the surface and settle into a glossy layer. Allow the pan to cool fully before slicing into squares.
