Preheat the oven to 350 degrees F (175 degrees C). Grease three (9-inch) round cake pans.
Step 2
Beat together brown sugar and 1 cup butter in a large bowl until creamy and smooth. Add eggs one at a time, mixing well after each addition. Beat in mashed bananas and 1 cup sour cream. Stir in flour, baking soda, and salt until well combined. Mix in nuts and 2 teaspoons vanilla until incorporated.
Step 3
Bake in the preheated oven until a toothpick inserted into the centers of cakes comes out clean, 30 to 40 minutes. Allow cakes layers to cool completely on wired racks.
Step 4
Beat confectioners' sugar, remaining 1/2 cup butter, and remaining 1/4 cup sour cream in a large bowl until well combined. Add remaining 1 teaspoon vanilla and beat until frosting is fluffy.