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["Heat oven to 375.", "Grease and flour two 8"" round cake pans lined with parchment paper cut to fit; set aside.", "In a bowl, whisk together flour, baking powder, ginger, salt, cinnamon, cloves, and mace; set aside.", "In the bowl of a stand mixer fitted with a paddle, beat 1/2 cup butter and brown sugar on medium-high speed until smooth, 12 minutes.", "Add eggs one at a time, mixing well after each addition until smooth.", "Add half the dry ingredients and mix until just combined.", "Add pumpkin and milk, and then add remaining dry ingredients; mix until smooth.", "Divide batter evenly between prepared pans and smooth tops with a rubber spatula; bake until a toothpick inserted in center of cakes comes out clean, about 30 minutes.", "Transfer to a rack and let cool for 30 minutes; unmold cakes and let cool.", "In the bowl of a stand mixer, beat remaining butter and vanilla on medium speed until smooth.", "Add confectioners' sugar, 1 cup at a time, beating after each addition until smooth.", "Increase speed to high and beat until frosting is light and fluffy.", "Place 1 cake on a cake stand and frost the top with 1/3 of the frosting; stack second cake on top and frost top and sides with remaining frosting.", "Refrigerate cake; let cake sit for 1 hour at room temperature before serving."]