First, preheat the oven to 350 degrees Fahrenheit (175 degrees Celsius). Lightly grease two 8-inch round cake pans.
In a large mixing bowl, combine the grated carrots, flour, sugar, applesauce, oil, milk, and vanilla. Mix until well combined.
Then, add in the baking powder, baking soda, cinnamon, nutmeg, and salt to the bowl. Stir until fully incorporated.
Divide the batter evenly between the two greased cake pans. Smooth the top with a spatula.
Bake in the preheated oven for 30 to 33 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Remove the cakes from the oven. Let them cool for 10 minutes. Then, transfer to a wire rack to cool completely.
While the cakes are cooling, make the frosting. In a mixing bowl, beat the vegan cream cheese and vegan butter until creamy.
Gradually add the powdered sugar to the bowl, mixing well after each addition. Continue beating until the frosting is light and fluffy.
Stir in the vanilla until well combined.
Once the cakes have cooled completely, place one layer on a serving plate or cake stand. Spread a generous layer of frosting evenly on top of the cake.
Carefully place the second cake layer on top. Spread the remaining frosting over the top and sides of the cake.
Sprinkle chopped nuts on top if desired.
Finally, slice and serve!