Preheat oven to 350° and line a muffin pan with cupcake liners.
In a large bowl whisk together Flour, Sugars, Baking Oowder, Baking Soda, Salt, Cinnamon, and Nutmeg.
Stir in Vegetable Oil and add eggs one at a time till well combined.
Stir in Vanilla Extract and Milk.
Add Carrots and nuts if using, and stir until combined.
Divide batter equally into cupcake liners. Bake for 20 minutes or until a toothpick inserted comes out clean or with moist crumbs.
Allow to cool completely before frosting.
Cream Cheese Frosting
Combine Butter and Cream Cheese in a bowl and beat until creamy, well combined, and lump free.
Add Vanilla Extract and stir well to combine.
Gradually add powdered sugar till completely combined.
Notes
First note, if you want smaller pieces of carrot in your cupcake you can dice your grated carrots a bit to make them smaller. Just be careful cause you can release too much carrot juice by doing this, and it will make a more carrot tasting cupcake and mess with your baking time.Second note, if you want just a thin layer of frosting, cut the frosting recipe in half. If you use the entire recipe, you can actually pipe it on nice and thick. It's really up to you!