Preheat your oven to 350°F (175°C) and generously grease two 9-inch round cake pans with butter or non-stick spray.

In a medium bowl, whisk together the flour, baking soda, ground cinnamon, nutmeg, and salt until well combined and lump-free.

In a separate large mixing bowl, beat the eggs and granulated sugar together until the mixture is pale and slightly thickened, then slowly whisk in the vegetable oil.

Gradually stir the dry flour mixture into the wet egg mixture until just combined, being careful not to overmix the batter.

Fold in the grated carrots and chopped walnuts using a spatula until they are evenly distributed throughout the thick batter.

Divide the batter evenly between the two prepared cake pans and smooth the tops with the back of a spoon.

Bake in the preheated oven for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean.

Remove the cakes from the oven and let them cool in the pans for 10 minutes before transferring them to a wire rack to cool completely.

To make the frosting, beat the softened cream cheese and butter together in a bowl until smooth and creamy.

Gradually add the powdered sugar and vanilla extract, beating on low speed until combined, then increase to high speed until fluffy.

Once the cakes are fully cooled, spread a layer of frosting on top of one cake, place the second cake on top, and cover the top and sides with the remaining frosting.

Garnish with extra chopped walnuts if desired, slice into wedges, and serve this delightful dessert with a cup of coffee or tea.