Preheat the oven to 350°F (175°C). Grease and flour two 8-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 1/2 cup softened butter and granulated sugar together until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition. Mix in 1 teaspoon vanilla extract.
Add the mashed bananas to the wet mixture and mix until combined.
Alternately add the dry ingredients and buttermilk to the wet ingredients, beginning and ending with the dry ingredients. Mix until just combined.
Divide the batter evenly between the prepared cake pans and smooth the tops.
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 allow them to cool in the pans for 10 minutes.
Turn the cakes out onto wire racks and cool completely before frosting.
To make the frosting, beat the 1/4 cup softened butter until creamy.
Gradually add the powdered sugar and continue beating until smooth.
Mix in 1 teaspoon vanilla extract and 2 tablespoons heavy cream until the frosting is light and fluffy.
Place one cake layer on a serving plate and spread a layer of frosting on top.
Place the second cake layer on top and frost the top and sides of the cake evenly.
Refrigerate the cake for at least 30 minutes before serving to set the frosting.