Preheat oven to 375 degrees.
Line muffin cups with cupcake liners.
In a large mixing bowl, stir together the flour, brown sugar, white sugar, baking soda, baking powder and cinnamon.
In a separate bowl, beat together the eggs, vegetable oil and milk.
Add the liquid ingredients to the dry ingredients and stir together to combine.
Stir in the grated carrots.
Fill muffin cups 2/3 full.
Bake for 18 to 20 minutes, until a toothpick inserted in the center comes out clean.
While cupcakes are baking, combine cream cheese, butter and vanilla extract in a mixing bowl. Beat with an electric mixer until creamy.
Add powdered sugar, one cup at a time, to reach desired consistency and sweetness.
Remove cupcakes from oven and cool.
Spread frosting on top of each cupcake and serve.