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1
Make cupcakes:
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2
Preheat oven to 350F with rack in middle.
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3
Line muffin cups with paper liners.
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4
Coarsely grate enough carrots to measure 2 cups using large teardrop holes of a box grater.
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5
Whisk together flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg in a bowl.
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6
Whisk together oil, eggs, brown sugar, grated carrots, and vanilla in a large bowl, then stir in flour mixture until just combined.
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7
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.
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8
Cool in pan on a rack 10 minutes.
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9
Remove cupcakes from pan and cool completely on rack, about 1 hour more.
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10
To make the icing: Sift confectioners sugar into a bowl.
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11
Whisk in zest and 2 tablespoons juice until smooth.
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12
If icing is too thick, add more juice, 1 teaspoon at a time.
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13
Dip top of each cupcake into icing, letting excess drip off.
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14
Let icing set, about 15 minutes.
