Preheat oven to 350°.
Place carrots in a food processor; process until finely minced.
Combine carrots, sugar, oil, buttermilk, and eggs in a large bowl. Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, soda, and salt, stirring with a whisk. Add flour mixture to carrot mixture; stir until smooth. Stir in chocolate.
Spoon batter into 22 muffin cups lined with paper liners. Bake at 350° for 22 minutes or until a wooden pick inserted in center comes out clean. Cool in pan 10 minutes on a wire rack, and remove from pan. Cool completely on wire rack. Dust the cupcakes with powdered sugar.