Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, cream the softened butter and granulated sugar together with an electric mixer until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract.
In a separate small bowl, combine the mashed bananas, buttermilk, and sour cream.
Alternately add the flour mixture and the banana mixture to the butter mixture, beginning and ending with the flour mixture. Mix until just combined; do not overmix.
Divide the batter evenly between the prepared cake pans and smooth the tops with a spatula.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cakes from the oven and let them cool in the pans for 10 minutes. Then, turn the cakes out onto wire racks to cool completely.
To prepare the frosting, beat the softened butter with an electric mixer until creamy.
Gradually add the powdered sugar, beating on low speed until combined.
Add the heavy cream, vanilla extract, and salt. Beat on high speed for 3-4 minutes until the frosting is light and fluffy.
Once the cakes are completely cooled, place one cake layer on a serving plate. Spread a generous layer of frosting over the top.
Place the second cake layer on top and frost the top and sides of the cake evenly.
Slice and serve the banana cake layered immediately or refrigerate until ready to serve.