Carrot Cupcakes with Orange Icing
['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']
Preheat oven to 350°F with rack in middle. Line muffin cups with paper liners.
Coarsely grate enough carrots to measure 2 cups using large teardrop holes of a box grater.
Whisk together flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg in a bowl.
Whisk together oil, eggs, brown sugar, grated carrots, and vanilla in a large bowl, then stir in flour mixture until just combined.
Divide batter among muffin cups and bake until golden and a wooden pick inserted into center of a cupcake comes out clean, 20 to 25 minutes.
Cool in pan on a rack 10 minutes. Remove cupcakes from pan and cool completely on rack, about 1 hour more.
Sift confectioners sugar into a bowl. Whisk in zest and 2 tablespoons juice until smooth. If icing is too thick, add more juice, 1 teaspoon at a time. Dip top of each cupcake into icing, letting excess drip off. Put a carrot curl on top of each and let icing set, about 15 minutes.
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