Peel the carrots and then grate them over the large holes of a box grater or use the grating blade in a food processor. Transfer the grated carrots to a large bowl and set aside.

Preheat oven to 350 degrees F and place oven rack in center of oven. Apply butter to two – 9 x 2 inch cake pans and line the bottoms of the pans with a circle of parchment paper, grease the paper and then flour the pans, shaking off any excess flour. Set aside.

In a medium bowl, add flour, baking soda, salt, cinnamon and nutmeg. Whisk until thoroughly combined. Set aside. In the bowl of a stand mixer fitted with the paddle attachment or with a hand mixer, add the oil, sugar and vanilla and mix until combined. Add the applesauce and mix thoroughly. Scrape the bottom and sides of the bowl with a rubber spatula.

Crack the eggs into a small bowl or measuring cup and beat them lightly. With the mixer on low, gradually pour the beaten eggs in the oil, applesauce, and sugar mixture. Turn the mixer up to medium-high and beat for 3 minutes, until the mixture is pale yellow. Scrape the bottom and sides of the bowl at least once.

With the mixer on low, add the dry ingredients and mix just until the flour begins to disappear. Use a large rubber spatula and scrape the sides and bottom of the bowl. Do not over mix.

To the bowl of grated carrots, add the chopped walnuts or pecans. Toss the mixture with your hands to thoroughly combine. Dump the carrot mixture into the batter. Using a large rubber spatula, gently fold the carrot mixture into the batter to combine. Do not stir or over mix.

Divide batter evenly between the cake pans. Bake for about 35-40 minutes or until a tooth pick or tester inserted into the center of the cake comes out clean or the top of the cake springs back when touched gently.

Set the pans on a wire rack to cool for 5 minutes and then run a knife around the edge of the pans to release. Turn the cakes out on to a wire rack to cool completely. Once cooled cakes can be frosted with cream cheese frosting.

Make Ahead – Storage: Unfrosted cakes can be wrapped in plastic wrap and refrigerated or stored at room temperature overnight. Freeze Carrot Cakes: Properly wrapped cakes can be stored in freezer bags and frozen for up to 2 months. Thaw carrot cakes in the refrigerator overnight, before frosting.

Cream Cheese Frosting Instructions:

Add the softened cream cheese to the bowl of a stand mixer fitted with the paddle attachment or using a hand mixer. Beat for about a minute, until smooth. Add the softened butter and mix on medium speed to combine. Scrape bowl as needed. Add the vanilla extract and mix until combined.

With the mixer on low, gradually add the powdered sugar. Beat on medium speed until thoroughly mixed, smooth and creamy, about 3 minutes. Add more powdered sugar if needed to reach desired consistency.

Assemble the Carrot Cake: Place a dab of frosting on the center of the cake stand or serving dish. Remove the parchment paper from the first cake layer and place the cake onto your serving plate with the flat side up (the side that had the parchment paper on it).

Once firm, frost the cake with remaining cream cheese frosting. Garnish with additional chopped walnuts by gently patting them into the frosting around the sides of the cake with the palms of your hands, if desired.