Preheat the oven to 350?F (175?C) and line a muffin tin with cupcake liners.

In a large mixing bowl, whisk together the flour, granulated sugar, brown sugar, baking powder, baking soda, salt, cinnamon, and nutmeg.

In another bowl, mix the oil and eggs until well combined. Stir in the grated carrots and walnuts if using.

Combine the wet ingredients with the dry ingredients and mix until just combined.

Divide the batter evenly among the cupcake liners, filling each about 2/3 full.

Bake for 18-20 minutes or until a toothpick inserted into the center comes out clean.

Allow the cupcakes to cool completely before frosting.

In a mixing bowl, beat the softened cream cheese and butter together until smooth and creamy.

Gradually add the powdered sugar and vanilla extract, mixing until well combined and fluffy.

Frost the cooled cupcakes with the cream cheese frosting using a spatula or piping bag.