Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.

In a large mixing bowl, sift together flour, baking soda, cinnamon, nutmeg, and salt. Whisk until evenly combined.

In a separate bowl, whisk together brown sugar, vegetable oil, eggs, vanilla extract, and sour cream until smooth.

Gradually add the dry mixture to the wet, stirring gently until just combined.

Fold in the grated carrots gently into the batter until evenly distributed.

Divide the batter between the prepared pans and bake for 30 to 40 minutes, or until a toothpick comes out clean.

Remove from oven and let cool in pans for about 10 minutes, then transfer to wire racks to cool completely.

For frosting, beat together cream cheese and butter until creamy, gradually add powdered sugar and vanilla extract.

Frost cooled cakes, layering them and smoothing the frosting for a clean finish.

Chill if necessary, then slice and serve.