Ingredients

• 1 stick (1/2 cup) unsalted butter, softened, plus additional for greasing pan
• 1 1/2 cups all-purpose flour plus additional for dusting pan
• 1 1/2 teaspoons baking powder
• 1/2 teaspoon baking soda
• 1/2 teaspoon salt
• 3/4 cup packed light brown sugar
• 1 large egg
• 3/4 cup well-mashed very ripe bananas
• 1/4 cup sour cream
• 1/2 teaspoon vanilla
• 3 oz cream cheese, softened
• 3 tablespoons unsalted butter, softened
• 1/3 cup confectioners sugar
• 3 tablespoons well-stirred canned cream of coconut such as Coco López (not coconut milk)
• 1 teaspoon dark rum (optional)
• 1/3 cup sweetened flaked coconut

Instructions

1. Put oven rack in middle position and preheat oven to 350°F.
2. Lightly butter and flour a 9-inch round cake pan, knocking out excess flour.
3. Whisk together flour (1 1/2 cups), baking powder, baking soda, and salt in a small bowl.
4. Beat together butter (1 stick) and brown sugar in a large bowl with an electric mixer at high speed until pale and fluffy. Beat in egg until combined, then add bananas, sour cream, and vanilla and beat until combined well. Reduce speed to low and add flour mixture, mixing until just incorporated.
5. Spread batter in cake pan and bake until pale golden and a wooden pick or skewer inserted in center comes out clean, 20 to 25 minutes.
6. Cool in pan on a rack 10 minutes. Run a thin knife around edge of pan, then invert rack over cake and invert cake onto rack to cool completely.
7. Beat together cream cheese and butter in a bowl using cleaned beaters at medium speed until smooth. Reduce speed to low, then add confectioners sugar, cream of coconut, and rum (if using) and mix until combined. Increase speed to high and beat until light and fluffy, about 2 minutes.
8. Frost top of cooled cake and sprinkle with coconut.