Preheat oven to 350 degrees F (175 degrees C). Line 30 muffin cups with paper liners.

Whisk flour, 1 1/2 teaspoons cinnamon, baking powder, baking soda, allspice, and salt together in a bowl. Beat white sugar, brown sugar, and eggs together in another bowl until light and creamy. Add oil to sugar mixture and beat until combined. Gradually stir flour mixture into sugar mixture until batter is just-combined; fold in carrots. Spoon batter into prepared muffin cups, filling each 3/4 full.

Bake in the preheated oven until a toothpick inserted into the center of a cupcake comes out clean, 18 to 22 minutes. Cool in the pans for 5 minutes before transferring to a wire rack to cool completely.

Beat cream cheese and butter together in a bowl until light and fluffy. Add confectioners' sugar 1 cup at a time, beating well after each addition, until desired frosting consistency is reached. Beat 1 teaspoon cinnamon into frosting. Spread frosting over cooled cupcakes.