Combine flour, soda, salt, and spices in a small mixing bowl.
Combine oil, eggs, and sugar; beat well. Add flour mixture; beat well. Stir in carrots.
Spoon batter into paper-lined muffin pans, filling only two-thirds full. Bake at 350° for 25 minutes or until cupcakes test done. Cool in pan 10 minutes;
remove to wire racks to cool completely. Split each cupcake vertically through the center, leaving paper intact. Spoon 1 tablespoon frosting into each cupcake.