Reduce the Apple Cider: In a small saucepan over medium heat, simmer the apple cider until it reduces to exactly ½ cup. This should take about 10 to 15 minutes. Set it aside to cool completely before using in the batter.
Prepare Oven and Pan: Preheat your oven to 350°F (175°C). Generously grease and flour a 10-cup Bundt pan, or use a non-stick baking spray with flour to ensure the cake releases easily after baking.
Mix Dry Ingredients: In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg until well combined. This ensures the spices and leavening agents are evenly distributed.
Cream Butter and Sugars: In a large bowl or stand mixer, beat the softened butter, granulated sugar, and brown sugar together until light and fluffy. This usually takes about 3 to 4 minutes of high-speed mixing.
Add Wet Ingredients: Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract and the cooled, reduced apple cider until the mixture is smooth.
Combine the Batter: Gradually add the dry ingredients to the butter mixture, alternating with the buttermilk. Start and end with the dry ingredients. Mix until just combined, being careful not to overmix the batter.
Bake the Cake: Pour the batter into the prepared Bundt pan and smooth the top with a spatula. Bake for 40 to 50 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool in the pan for 10 minutes before inverting it onto a wire rack.
Add the Cinnamon Coating: While the cake is still warm, brush the entire surface with the 4 tablespoons of melted butter. Mix the coating sugar and cinnamon together, then generously sprinkle or press the mixture onto the cake until fully coated.