Reduce apple cider: Pour the apple cider into a small saucepan over medium-high heat. Bring cider to a boil, stirring occacionally. It will bubble up and then start to settle down. Continue boiling until the cider is reduced to about 1/2 cup. Remove from heat and transfer to a heat-safe bowl to cool.
Preheat oven to 350 degrees F.
Sift together flour, cinnamon, nutmeg, salt, and baking powder into a medium-sized mixing bowl. Set aside.
Using a stand mixer with a paddle attachment, beat together the oil and sugars until combined. Scrape the bowl and add apple sauce, beat to combine. With the mixer on slow speed, add eggs one at a time, waiting for each to just disappear before adding the next. Scape the bowl.
Add 1/3 of the flour mixture and beat until barely combined, then add 1/2 of the reduced apple cider, the next 1/3 of the flour mixture, the rest of the apple cider, and then the rest of the flour. Do not overmix the batter, a few streaks of flour are okay.
Toss the grated apple in about 1 tablespoon of flour and sprinkle on top of the batter. Use a spatula to gently mix the apples in with the batter (trying to break up lumps of apple).
Spray your 10-cup bundt pan with nonstick spray or the magic paste (see notes). Transfer batter to the prepared pan and bake for 50-55 minutes or until a toothpick inserted comes out clean.
Remove the cake from the oven, and let the cake cool in the bundt pan for about 10 minutes. Then invert the cake on to a cooling rack to cool completely. Set aside.