Coconut Rum Cake
1-1/4 cups all-purpose flour
1-1/2 teaspoons baking powder
1/4 teaspoon salt
4 large eggs plus 3 large yolks
1-1/2 cups sugar
1 teaspoon pure vanilla extract
1-1/2 sticks unsalted butter, melted and cooled
3/4 cup well-stirred sweetened cream of coconut
1 cup coconut, shredded
2 teaspoons confectioners sugar
3 tablespoons cream cheese, softened
3 tablespoons well-stirred sweetened cream of coconut
1 tablespoon dark rum
3/4 teaspoon pure vanilla extract
2 to 3 tablespoons heavy cream
1/2 cup confectioners sugar
Preheat oven to 350°F with rack in middle. Lightly butter cake pan and line bottom with a round of parchment paper. Lightly butter parchment, then flour pan.
Whisk together flour, baking powder, and salt.
Whisk together whole eggs and yolks, sugar, and vanilla in a large bowl. Gradually whisk in flour mixture until combined, then whisk in butter until just combined. Pour into cake pan and rap pan on counter to expel air bubbles.
Bake until golden brown and cake starts to pull away from side of pan, about 45 minutes. Cool in pan on a rack 10 minutes. (Leave oven on.) Invert cake onto rack (discard parchment) and cool 10 minutes more. Generously brush top and side of warm cake with cream of coconut, allowing it to soak in before brushing on more. Cool completely.
As cake cools: toss the coconut with the confectioners sugar, then spread in 1 layer on a baking sheet. Bake until just dry but not golden , 5 to 10 minutes. Cool coconut completely. (It will crisp as it cools.)
Make icing: Beat together cream cheese, cream of coconut, rum, vanilla, and 2 tablespoons cream with an electric mixer until smooth, then beat in confectioners sugar. Icing should be smooth and slightly runny; stir in remaining tablespoon cream if necessary.
Smooth icing over top of cooled cake, allowing some to drip over side, then top with coconut slivers.