HEAT oven to 375°F. Line 12 muffin cups with paper liners.
COMBINE carrots, flour, sugar, cinnamon, baking powder, baking soda and salt in large bowl. Add eggs, oil, applesauce and vanilla. Beat on medium speed until well combined (about 1 minute). Fill muffin cups about 3/4 full.
BAKE 20 to 25 minutes or until toothpick inserted in center comes out clean. Remove from pan; cool on wire rack.
FROST with Cream Cheese Frosting.