Preheat your oven to 350°F and grease and flour two 9-inch round pans.

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

In another bowl, beat eggs, vegetable oil, and vanilla extract until pale yellow and smooth.

Gently fold grated carrots into the wet mixture.

Divide batter between prepared pans and bake for 25–30 minutes.

Allow cakes to cool in pans for 10 minutes, then invert onto racks.

Beat cream cheese and butter until smooth, then add powdered sugar and vanilla.

Frost the cooled cake layers with the cream cheese frosting.