Preheat oven to 350°F. Toast the coconut in a dry skillet over medium heat, stirring constantly until golden, about 4 minutes. Transfer to a plate to cool. Reserve a few spoonfuls for the topping.

Cream the 1/2 cup butter and 1 cup sugar with a mixer until light and fluffy, about 3 minutes. Beat in the eggs one at a time, then the vanilla and coconut extracts.

In a separate bowl, whisk the flour, baking powder, and salt. Add the dry ingredients to the butter mixture in three parts, alternating with the buttermilk, starting and ending with dry. Fold in 1/2 cup of the toasted coconut by hand.

Pour batter into a greased 9-inch round pan. Bake 30 to 32 minutes, until a toothpick inserted in the center comes out with moist crumbs. Cool in the pan 10 minutes, then turn onto a wire rack to cool completely.

Beat the cream cheese and 2 tablespoons butter until smooth. Add powdered sugar, 1/2 teaspoon vanilla, and enough milk to reach a spreadable consistency. Frost the cooled cake and press the reserved toasted coconut over the top and sides.

Slice and serve. Store leftovers in the fridge.