To prepare cupcakes, place 2 muffin cup liners in each of 12 muffin cups; coat liners with cooking spray.
Weigh or lightly spoon flour into a dry measuring cup; level with a knife. Combine flour and next 3 ingredients (through salt) in a small bowl; stir with a whisk.
Combine 3/4 cup sugar and 2 tablespoons butter in a large bowl; beat with a mixer at medium speed until blended (mixture will be the consistency of damp sand). Add egg and egg white, one at a time, beating well after each addition. Add flour mixture and milk alternately to egg mixture, beginning and ending with flour mixture. Fold in coconut and vanilla.
Spoon batter evenly into prepared muffin cups. Bake at 350° for 18 minutes or until cupcakes spring back when touched lightly in the center. Cool in pan 2 minutes; remove from pan. Cool completely on wire rack.
To prepare frosting, combine 3 tablespoons butter and next 3 ingredients (through juice) in a medium bowl; beat with a mixer at medium speed until smooth. Gradually add the powdered sugar, beating just until smooth. Spread about 2 1/2 teaspoons frosting onto each cupcake.
Find potato starch in the supermarket baking aisle. Use lemon rind and fresh lemon juice in place of the lime for a variation.