This recipe was developed by Chef Pam McKinstry in 1978 for her restaurant on Nantucket Island, where it's still popular. (It's our best-selling dessert at the Farm Stand, too.) The cake is very moist, thanks to the carrots, and will keep, covered and refrigerated, for up to a week.
Position a rack in the lower third of the oven, and preheat the oven to 325 degrees F. Heavily grease and flour 2 round 9-inch cake pans. Set aside.
Whisk together the flour, sugar, cinnamon, salt, baking soda, and baking powder in a large bowl.
In a separate small bowl, whisk the eggs with the oil and vanilla. Add the egg mixture to the flour mixture and stir to combine. Add the carrots and 1 cup of the nuts, stirring just to blend.
Divide the batter between the 2 prepared pans. Bake until a toothpick inserted into the center of the cake comes out clean and the edges have pulled away from the sides of the pan, 60 to 70 minutes. Cool completely on a wire rack before unmolding.
To make the frosting, beat the cream cheese and butter in a medium-size bowl until very smooth and creamy. Gradually beat in the confectioner's sugar, then the vanilla. If the frosting is very stiff, thin with a tablespoon of milk or water.
Place one of the cake layers on a flat plate. Spread with some of the frosting. Top with the second layer and frost the sides and top of the cake. Sprinkle the top of the cake with the remaining nuts.