Preheat the oven to 350°F. Grease and flour two 9-inch layer cake pans.
Cream the butter and granulated sugar together in a mixing bowl. Add the egg yolks and beat well. Add the mashed bananas.
Sift the baking powder, baking soda, and salt together and add them to the butter mixture. Stir until just combined. Add the buttermilk and vanilla. Beat the egg whites to soft peaks. Fold gently into the batter.
Pour the batter into the prepared pans. Set on the center rack of the oven and bake until a cake tester inserted into the center comes out clean, 25 to 30 minutes. Cool in the pans on a rack for 10 minutes. Unmold and cool on a rack for 2 hours.
When cooled, place one layer on a serving plate and frost with the cream cheese frosting. Arrange slices of banana over the frosting; cover with the second layer and frost the top and sides of the cake.
Cover the sides of the cake with the chopped nuts, holding the nuts in your palm and pressing them firmly to the sides of the cake. Dust the top of the cake with confectioners’ sugar.