Carrot Cupcakes with Orange Icing

Name: Carrot Cupcakes with Orange Icing
Ingredients: 4 medium carrots; 1 1/2 cups all-purpose flour; 1 1/2 teaspoons baking powder; 1/2 teaspoon baking soda; 3/4 teaspoon salt; 1 teaspoon ground cinnamon; 1/2 teaspoon ground ginger; 1/4 teaspoon grated nutmeg; 3/4 cup vegetable oil; 3 large eggs; 1 cup packed light brown sugar; 1 teaspoon pure vanilla extract; 1 1/4 cups confectioners sugar; 1/2 teaspoon grated orange zest; 2 to 3 tablespoons fresh orange juice; Equipment: a muffin pan with 12 (1/2-cup) muffin cups; 12 paper liners; 12 paper liners; Garnish: candied carrot curls