Three layers of delicately spiced apple cake are filled and frosted with tangy cream-cheese frosting here, yielding a towering dessert worthy of any celebration.
Cake: Preheat oven to 350 degrees. Butter three 8-inch round cake pans; line with parchment. Butter and flour parchment, tapping out any excess.
In a medium bowl, whisk together flour, baking soda, baking powder, cinnamon, ginger, and salt. In a large bowl, whisk together butter, brown sugar, and eggs until well combined; fold in grated and diced apples. Add flour mixture; mix just until combined. Divide batter among prepared pans; smooth tops.
Bake until a tester inserted in centers comes out clean, 35 to 40 minutes. Let cakes cool in pans 20 minutes, then invert onto wire racks; remove parchment. Invert cakes again; let cool completely on racks.
Frosting: In the bowl of a mixer fitted with the paddle attachment, beat butter on medium-high speed until fluffy, about 2 minutes. Add cream cheese and beat until well combined and fluffy, about 2 minutes more. Add confectioners' sugar and salt; beat 5 minutes.
Place a cake layer on a serving plate. Spread about 1 cup frosting evenly over it; top with a second cake layer. Repeat with another 1 cup frosting and third cake layer. Spread remaining frosting over top and sides of cake. Refrigerate at least 1 hour and up to 4 days. Return to room temperature before serving. Garnish with apple chips, if desired; use a serrated knife to slice cake.
You can also bake the cake in a 9-by-13-inch pan; the baking time will be about the same.