Heat your oven to 375°F and grease a 9x13 inch baking pan with butter or cooking spray, making sure to coat the bottom and sides evenly. This prevents sticking and ensures even browning on the edges.

In a large mixing bowl, combine the softened butter, sugar, and sour cream, beating together until light and fluffy, about 2-3 minutes. This incorporates air into the batter and creates a better texture. Add the eggs one at a time, beating well after each addition to fully emulsify them into the mixture.

Stir the mashed bananas and 2 tsp vanilla extract into the wet mixture from Step 2 until well combined. The bananas should be mashed smooth with just some small lumps remaining for texture—this prevents the brownies from becoming gluey. Mix until you don't see any streaks of banana.

In a separate bowl, whisk together the flour, baking soda, salt, and cinnamon. Add this dry mixture to the banana mixture from Step 3 and mix gently for about 1 minute until just combined—don't overmix, as this can make the brownies tough. Fold in the chopped walnuts gently at the end. I like to fold rather than stir here because it keeps the walnuts from breaking apart and distributes them more evenly throughout.

Pour the batter from Step 4 into your prepared pan, spreading it evenly into the corners. Bake in the preheated 375°F oven for 20-25 minutes, until a toothpick inserted in the center comes out with just a few moist crumbs. The brownies should still be warm when you remove them from the oven—this is important for frosting them.

While the brownies bake, melt the 1/2 cup butter in a saucepan over medium heat, then continue cooking, swirling occasionally, until it turns golden brown and smells nutty, about 5-8 minutes total. Watch carefully to avoid burning. Remove from heat and let cool for 2-3 minutes, then whisk in the sifted powdered sugar, 1.5 tsp vanilla extract, and milk until smooth and spreadable. The frosting should be thick but pourable—if it's too thick, add milk a teaspoon at a time.

Spread the warm brown butter frosting from Step 6 evenly over the warm brownies from Step 5 immediately after removing them from the oven. The warmth helps the frosting set slightly and adhere better. Let cool completely at room temperature before cutting into squares and serving.