Preheat the oven to 350°F (175°C). In a mixing bowl, combine graham cracker crumbs, sugar, and melted butter. Mix until well combined.

Press the mixture firmly into the bottom of a 9-inch springform pan. Bake for 10 minutes, then remove from oven and let cool.

In a large mixing bowl, beat the softened cream cheese until smooth. Add sour cream and sugar, mixing until well combined.

Add eggs one at a time, mixing well after each addition. Stir in apple cider, vanilla extract, cinnamon, and nutmeg.

Pour the cheesecake filling over the cooled crust in the springform pan.

Bake in the preheated oven for 50-60 minutes, or until the center is set but slightly jiggly. Turn off the oven and leave the cheesecake inside for 1 hour.

Remove from the oven and let cool to room temperature, then refrigerate for at least 4 hours or overnight.

In a saucepan, combine diced apples, apple cider, brown sugar, and cinnamon. Cook over medium heat until the apples are tender, about 10-15 minutes.

Remove from heat and let cool slightly before serving over the cheesecake.

Remove the cheesecake from the springform pan and top with the apple compote before serving.