Preheat the oven to 325°F (160°C). Generously grease a 10 to 12-cup Bundt pan using butter or cooking spray, ensuring all crevices are coated. Lightly dust with flour, tapping out any excess.

In a medium bowl, whisk together the all-purpose flour, ground cinnamon, ground nutmeg, salt, baking powder, and baking soda. Set aside.

In a large mixing bowl, using an electric mixer on medium speed, beat together the granulated sugar, brown sugar, and vegetable oil until smooth and well blended. Incorporate the eggs one at a time, ensuring each is fully mixed before adding the next. Add the applesauce and vanilla extract, mixing just until combined.

With the mixer on low speed, gradually alternate adding the dry ingredient mixture and apple cider to the wet mixture, beginning and ending with the dry ingredients. Mix only until no streaks of flour remain. The batter will be slightly loose.

Pour the batter evenly into the prepared Bundt pan. Bake for 50 to 60 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake to cool in the pan for 15 to 20 minutes before carefully inverting onto a wire rack to cool completely.

In a small bowl, combine the granulated sugar and ground cinnamon. Once the cake has cooled, brush the entire surface with melted butter. Sprinkle and gently pat the cinnamon sugar mixture evenly over the cake until fully coated.

Slice the cake and serve as desired. Enjoy this delightful dessert as a cozy and sweet treat.