Preheat your oven to 350°F (175°C). Grease a 9-inch round cake pan and line the bottom with parchment paper for easy removal.
Prepare the dry ingredients. In a medium mixing bowl, whisk together the flour, baking soda, salt, cinnamon, ginger, and nutmeg. Set this bowl aside.
Mix the wet ingredients. In a large mixing bowl, beat the eggs until smooth. Add the grated apple, melted butter, oil, both sugars, apple butter, buttermilk, and vanilla extract. Stir until the mixture is well combined and smooth.
Combine wet and dry. Gradually add the dry ingredient mixture into the wet ingredients, stirring just until everything is incorporated. Be careful not to overmix.
Pour and bake. Pour the batter into the prepared cake pan and spread it evenly. Bake for 35–40 minutes, or until a toothpick inserted into the center comes out clean.
Cool the cake. Allow the cake to cool in the pan for 10–15 minutes, then transfer to a wire rack to cool completely before frosting.
Make the frosting. In a medium bowl, beat the cream cheese and butter together until creamy. Add the powdered sugar and apple pie spice. Beat until light, fluffy, and spreadable.
Frost and serve. Once the cake is fully cooled, spread the spiced cream cheese frosting over the top. Slice and serve.