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

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

In another bowl, mix the oil and eggs until well combined. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Fold in the grated carrots until evenly distributed.

Divide the batter evenly among the prepared cupcake liners, filling each about two-thirds full.

Bake in the preheated oven for 20-25 minutes, or until a toothpick inserted into the center of a cupcake comes out clean.

Remove from the oven and let cool in the pan for 5 minutes before transferring to a wire rack to cool completely.

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

Gradually add the powdered sugar, mixing until well incorporated.

Stir in the vanilla extract until combined and smooth.

Once the cupcakes are completely cool, frost each cupcake generously with the cream cheese frosting.