Preheat the oven to 350 degrees.
Grease and flour a 10-cup Bundt pan. Set aside.
In a medium bowl, sift the flour, baking soda, nutmeg, cinnamon and salt with a whisk. Set aside.
Add oil, vanilla, and sugar to a bowl of a stand mixer with the paddle attachment. Combine on medium speed for 2 minutes, or until all the ingredients are combined. (Alternatively, this can be made with a hand mixer.)
Add the eggs, one at a time, mixing well after each addition.
Turn the mixer to low and add the apple butter and reduced apple cider. Turn the speed up a notch and combine well.
Turn the mixer back to low and add the dry ingredients and shredded apple. Combine on low until no more flour is seen. Remove the bowl from the mixer. Using a silicone spatula, stir the batter from the bottom of the bowl gently to makes sure all the ingredients are combined well.
Scrape the batter into the greased Bundt pan and bake for 45 minutes to 1 hour. Begin checking with a toothpick test as early as 45 minutes. Bake until a toothpick inserted into the cake comes out with a few moist crumbs.
Remove the cake from the oven and allow it to cool for 20 minutes at room temperature.
While the cake is cooling, combine all the frosting ingredients in a medium bowl with a wire whisk until the frosting is smooth. Set aside until ready to use. (If not using the day of, cover and refrigerate. Bring to room temperature before using.)
Invert the cake onto a flat platter or cake stand and let it cool if you are frosting right away. You can serve the cake still warm with a dusting of powdered sugar.
Once cool, frost with the cream cheese frosting.
Keep leftovers in an air-tight container in the refrigerator for up to 3 days for best quality.