In a medium bowl, combine all-purpose flour, baking soda, baking powder, salt, ground cinnamon, and ground nutmeg. Set aside.

In a large bowl, whisk together the oil, brown sugar, and granulated sugar until well combined. Whisk in eggs, one at a time, and vanilla extract until well combined.

With a spatula, fold dry ingredients into the batter until well incorporated. Stir in the grated carrots.

Divide the batter between the prepared cake pans. Bake until the tops of the cake layers are springy when touched and when a toothpick inserted into the center of the cake comes out clean for 40 to 45 minutes.

Cool cakes in pans for 15 minutes then turn out onto cooling racks, peel off the parchment paper and cool completely.

In a large bowl using a handheld or stand mixer fitted with a paddle attachment. Beat the cream cheese and butter together on medium-high speed until smooth.

Beat in the powdered sugar, a 1/4 cup at a time until fluffy. Adjust the sweetness to your liking. Beat in heavy cream and vanilla extract until well incorporated. Chill covered until ready to frost cake.

When the cake layers are completely cool, level the tops of each cake with a knife or cake leveler. Place one cake layer on your cake stand or serving plate. Evenly cover the top with frosting. Place the second layer and frost the top again. Place the third layer and spread the remaining frosting all over the top and sides. Crumb coat the side of the cake and decoratively pipe the border-top of the cake using a round piping tip with remaining frosting.

Scatter the toasted walnuts on the top center of the cake and place rosemary sprigs for decoration.