Banana Coconut Rum Cake

Cake

2 cups cake flour
2 1/4 teaspoons baking powder
1/8 teaspoon baking soda
1/8 teaspoon salt
10 tablespoons (1 1/4 sticks) unsalted butter, room temperature
1 cup sugar
2 egg yolks
1 tablespoon vanilla extract
1/2 cup plus 2 tablespoons milk, room temperature
1 cup mashed very ripe bananas
1/3 cup sweetened shredded coconut
3 large egg whites, room temperature

Frosting

1 1/2 cups (3 sticks) unsalted butter, room temperature
4 cups powdered sugar
3/4 cup mashed very ripe banana
4 tablespoons dark rum
1 tablespoon vanilla extract
1 teaspoon fresh lemon juice
1 1/2 cups sweetened shredded coconut

For Cake: Position rack in center of oven and preheat to 350 degrees. Butter and flour two 8-inch diameter cake pans. Sift flour, baking power, baking soda, and salt into medium bowl. Cream butter and sugar in large bowl until light. Add yolks and vanilla and beat until combined. Gradually beat in dry ingredients alternately with milk and bananas in 3 additions each. Continue beating 2 minutes. Beat in coconut.

Using electric mixer fitted with clean dry beaters, beat whites in
medium bowl to medium-stiff peaks. Gently fold in whites into batter
in 2 additions. Divide batter between prepared pans. Bake until cakes are just golden and tester inserted into center of each comes out clean, about 30 minutes. Cool cakes in pans on rack 10 minutes. Run small, sharp knife around pan sides to loosen cakes if necessary. [Can be prepared one day ahead. Cover with plastic and let stand at room temperature.]

For Frosting: Cream butter in large bowl until light. Sift half of sugar over and beat until fluffy. Add mashed bananas, 1 tablespoon rum, vanilla extract, and lemon juice, and beat to combine. Sift remaining half of sugar over and beat until thick.

Place 1 cake layer on plate. Pierce cake all over with tip of knife.
Sprinkle 1 1/2 tablespoons rum over cake. Spread 1 1/2 cups frosting
over. Top with second cake layer. Pierce cake all over with tip of
knife. Drizzle remaining 1 1/2 tablespoons rum over. Spread remaining frosting over top and sides of cake. Press coconut onto top and sides of cake, covering completely. [Can be prepared four hours ahead. Cover with plastic wrap and let stand at room temperature.]