Preheat oven ot 350 degrees F. Spray a 12 cup muffin tin with non-stick spray or line the tin with muffin liners.
Add flour, baking soda, white sugar, brown sugar, cinnamon, nutmeg, and salt to a medium mixing bowl and whisk together until combined.
Make a well in the center of the dry ingredients and add the oil, egg, and vanilla. Mix until just combined.
Add in the shredded carrots and fold until incorporated.
Divide the batter evenly among the 12 muffins. Fill about ⅔ of the way full to keep the muffins from overflowing while baking.
Bake muffins for 18-20 minutes, or until a toothpick comes out clean when placed in the center of a muffin.
Allow to cool on a wire rack for 10 minutes.
While cooling, whisk up the cream cheese icing ingredients in a small bowl. Whisk until the lumps are gone.
Drizzle with a cream cheese icing, if desired. You may also turn your muffins upside down and dip them in the glaze. Enjoy!