For the cupcakes: Whisk 1 1/3 cups flour, 1 teaspoon baking powder and 1/2 teaspoon salt. In a separate bowl, beat 1 stick softened butter and 1 cup granulated sugar with a mixer on medium-high speed until fluffy, 4 minutes. Beat in 2 eggs, one at a time, then 1/2 teaspoon coconut extract. Beat in the flour mixture on low speed in three batches, alternating with 1/2 cup unsweetened coconut milk. Beat on medium-high speed until just combined. Divide among 12 lined muffin cups. Bake at 350˚ until the tops spring back when pressed, 20 to 25 minutes. Let cool 5 minutes in the pan, then remove to a rack to cool completely.
For the frosting: Pulse 2 sticks softened butter, 2 cups confectioners’ sugar, 8 ounces melted white chocolate and 3 tablespoons unsweetened coconut milk in a food processor until smooth. Frost the cupcakes. Top with shredded coconut.