Vanilla Bean-Coconut Cupcakes With Frosting

Ingredients

• 2 13- to 14-ounce cans unsweetened coconut milk (preferably organic)
• 2 cups all purpose flour
• 2 1/4 teaspoons baking powder
• 1/2 teaspoon salt
• 3/4 cup (1 1/2 sticks) unsalted butter, room temperature
• 1 1/3 cups sugar
• 3 large eggs
• seeds scraped from 1 split vanilla bean or 1 1/2 teaspoons vanilla extract
• 1 cup reduced coconut milk (see above), room temperature
• 1 cup (2 sticks) unsalted butter, room temperature
• 2 1/2 cups powdered sugar
• 1/3 cup reduced coconut milk (see above), room temperature
• seeds scraped from 1 split vanilla bean or 1 1/2 teaspoons vanilla extract
• 1/8 teaspoon salt
• 1 1/2 cups sweetened flaked coconut, lightly toasted (for garnish)