1Preheat oven to 350 degrees F (175 degrees C). Grease the bottoms only of 12 muffin cups, or line with baking cups. Sift together the flour, cinnamon, baking soda, baking powder, and salt; set aside.
2Beat the eggs and sugar until frothy and lightened in color. Stir in the oil, vanilla extract, and grated carrot; fold in the flour mixture. Pour the batter into the prepared muffin tins.
3Bake in preheated oven until toothpick inserted in center comes out clean, 15 to 20 minutes. Remove to cool on wire racks.
4Meanwhile, prepare the icing by beating together the cream cheese, butter, vanilla, and confectioners' sugar until fluffy. Frost the cooled muffins and chill until ready to serve.