3tablespoonsmilk or half and halfmore or less depending on desired thickness
Instructions
To make the banana bars:
In a saucepan over medium heat, melt 1/2 cup unsalted butter. Whisk frequently, scraping the bottom. As the butter foams, continue whisking and scraping to release any brown bits that may stick to the bottom. Once the butter has sufficiently browned (not burned) and smells heavenly, remove from heat.
Preheat oven to 375°F. Line a 15½ x 10½ inch jelly roll pan with parchment paper or grease with butter.
Add browned butter, 1 1/2 cups sugar, 1 cup sour cream, and 2 eggs to the bowl of a stand mixer. Using the paddle attachment, mix on low speed for about a minute. Scrape sides, add 1 1/2 cups bananas and 1 tablespoon vanilla, and continue to mix on low for another 30 seconds.
In a separate bowl, combine 2 cups all-purpose flour, 1 teaspoon salt, and 1 teaspoon baking soda. Add dry ingredients to the wet. Start mixing on low speed just to combine and then flash on high speed for about 10 seconds to fully mix. Scrape sides, add 1/2 cup chopped walnuts, and mix to combine.
Spread batter in pan and bake in preheated oven until light brown, about 20 to 25 minutes.
To make the frosting:
In a saucepan over medium heat, melt the 1/2 cup unsalted butter with the 2 vanilla beans. Whisk frequently, scraping the bottom as well as the insides out of the vanilla bean. As the butter foams, continue whisking and scraping to release any brown bits that may stick to the bottom. Once the butter has sufficiently browned (not burned) and smells heavenly, remove from heat. Remove vanilla bean pods from butter and scrape and remaining seeds using a sharp pairing knife to return to the butter.
Using the whisk attachment on your stand mixer, beat browned vanilla bean butter with the 3 cups confectioner's sugar. Start slow to incorporate and then turn the speed up to medium and then high until the frosting is light and fluffy.
One tablespoon at a time, add the 3 tablespoons milk or half and half (I used half and half) and continue beating the frosting until you've reached the desired consistency.
Frost and serve:
Allow bars to fully cool before you frost with brown butter vanilla bean frosting and cut into individual servings.
Notes
These store really well in an airtight container in the freezer.