FOR THE CAKE: Preheat the oven to 350°F with racks in the upper and lower thirds of the oven.
Butter and flour two 8-inch round cake pans. Line the bottoms of the pans with parchment paper; butter and flour the parchment.
In a small bowl, whisk together the flour, baking soda, cardamom, cinnamon, ginger, salt, and allspice.
With a mixer, beat the melted butter and granulated sugar until well combined. Add in the eggs, one at a time, beating well after each addition. Fold in the flour mixture. Fold in the carrots and cashews.
Divide the batter between the pans, tapping them on the counter to get rid of any air bubbles. Bake for 30 minutes, switching the pans from top to bottom halfway through, until a toothpick inserted in the center of each cake comes out clean. Cool for 10 minutes in the pans; then invert the cakes onto a rack to cool completely.
TO ASSEMBLE THE CAKE: With a long serrated knife, cut each cake in half horizontally. Place four strips of wax paper on the plate, overlapping and covering the edges. Place one cake layer on the cake plate, cut side up, making sure the wax paper is underneath the cake (this will keep the plate clean as you frost the cake). Frost the bottom layer, top with another layer, cut side up, frost that, and continue until you’ve placed the last layer, cut side down, on top. Frost the top and sides.
VARIATION: To make carrot cupcakes (2 dozen): Spoon the batter into 24 paper-lined standard muffin cups. Bake at 350°F for about 30 minutes, or until a toothpick inserted in the center of a cupcake comes out with just a few moist crumbs attached. Cool for 5 minutes in the pans; then transfer to a rack to cool completely. You can serve them as they are, dusted with confectioners’ sugar, or spread with the cream cheese frosting.
FOR THE FROSTING: With a mixer, beat the cream cheese and butter until light, fluffy, and smooth. Beat in the confectioners’ sugar and vanilla until well combined.
Recipe courtesy of The Beekman 1802 Heirloom Cookbook by Dr. Brent Ridge and Josh Kilmer-Purcell with Sandy Gluck/Sterling Epicure, 2011.