Reduce the Apple Cider: Pour the apple cider into a small saucepan and bring it to a gentle simmer. Cook until it has reduced by about half and the apple flavor becomes concentrated. Remove from the heat and let it cool completely.
Prepare the Crust: Preheat the oven to 325°F. Combine the graham cracker crumbs, melted butter, granulated sugar, and salt. Press the mixture firmly into the bottom of a 9-inch springform pan. Bake until lightly golden, then remove and let cool.
Beat the Cream Cheese: Add the softened cream cheese to a large mixing bowl. Beat until smooth and creamy. Add the granulated sugar and brown sugar, then mix until well combined.
Add the Apple Cider and Flavorings: Add the cooled apple cider reduction, sour cream, vanilla extract, cinnamon, nutmeg, and salt. Mix gently until the filling is smooth and evenly combined.
Add the Eggs: Add the eggs one at a time, mixing gently after each addition. Stop mixing as soon as each egg is incorporated to avoid adding too much air to the batter.
Pour the Filling Over the Crust: Pour the cheesecake filling over the cooled crust. Gently tap the springform pan against the counter to release large air bubbles. Smooth the top with a spatula.
Bake the Cheesecake: Place the cheesecake in the preheated oven and bake until the edges are set while the center still has a slight jiggle. Avoid overbaking, as the cheesecake will continue to firm as it cools.
Cool Slowly: Turn off the oven and allow the cheesecake to cool gradually. Remove it from the oven and let it cool completely on a wire rack before refrigerating.
Chill Thoroughly: Cover the cooled cheesecake and refrigerate for at least 6 hours, preferably overnight. Chilling allows the cheesecake to fully set and develop its creamy texture.
Decorate and Serve; Remove the chilled cheesecake from the springform pan. Top with whipped cream, a sprinkle of cinnamon, apple cider reduction, and thinly sliced apples. Slice with a sharp, clean knife and serve chilled.