Step 1

Preheat oven to 325°. Butter two 8"-diameter cake pans with sides 2" high. Line bottoms of pans with parchment paper rounds. Whisk flour, baking soda, and salt in a large bowl. Using an electric mixer, beat 1 1/2 cups butter and sugar in another large bowl until light and fluffy, 2–3 minutes. Add eggs one at a time, beating to blend between additions. With mixer on low, gradually beat in flour mixture, scraping sides of bowl. Mix in bananas, then sour cream. Divide batter between pans.

Step 2

Bake cakes until a tester inserted into the center comes out clean, 50–55 minutes. Let cool for 20 minutes in pans on wire racks.

Step 3

Invert cakes onto wire racks; let cool completely. Remove parchment. Using a serrated knife, trim off rounded tops.

Step 4

Using an electric mixer, beat first 5 ingredients in a large bowl until light and fluffy, 6–7 minutes.

Step 5

Place 1 cake on a plate. Spread 1 cup frosting over. Arrange banana slices on top. Top with second cake. Spread a thin layer of frosting over top and sides of cake; chill for 30 minutes. Spread remaining frosting over top and sides of cakes.