In a large bowl, sift in the flour and then add brown sugar, sugar, cinnamon, nutmeg, baking powder, baking soda, and salt. Whisk until everything is combined.
In a medium bowl whisk together apple cider, applesauce, oil, eggs, and vanilla.
Gradually stir the wet mixture into the flour mixture, mixing until just combined. Avoid overmixing. Overmixing your batter can produce a tough and dry cake.
Preheat the oven to 350°F and spray a bundt pan with non-stick spray, or spread some butter as I do, and then dust with flour.
Pour the batter into the prepared pan. Bake for 40-45 minutes or until a toothpick in the center comes out clean.
Allow the cake to cool for 15 minutes, then turn it out onto a cooling rack. I place a piece of Parchment Paper (Baking Sheets) to prevent a mess when coating the cake.
Once the cake has slightly cooled (about 30 minutes), proceed to make the coating and topping.