In a small saucepan, bring 1 cup apple cider to a low simmer. Simmer for 5-7 for minutes, stirring occasionally, until reduced to ½ cup. Set aside to cool slightly. Preheat oven to 350°F. Grease and flour a 10–12 cup Bundt pan.
In a medium bowl, whisk together flour, baking powder, baking soda, corn starch, salt and cinnamon. In a large mixing bowl, beat the butter, granulated sugar, and brown sugar until light and fluffy. Add eggs one at a time, then mix in vanilla.
On low speed, add the dry ingredients in three additions, alternating with the reduced cider in two additions (starting and ending with dry). Fold in the applesauce until just combined. Spread batter evenly in the Bundt pan. Bake for 45–60 minutes, until a toothpick inserted in the center comes out clean or with just a few crumbs.
Cool the cake in the pan for 10 minutes, then invert onto a wire rack. While still warm, brush the cake with melted butter and sprinkle (or pat) cinnamon sugar all over until fully coated. Slice and enjoy warm or at room temperature. Store in an airtight container for up to 2 days, or freeze slices for longer storage.