Preheat oven to 350°F (175°C).
In a medium bowl, combine graham cracker crumbs, melted butter, and sugar. Mix well until evenly moistened.
Press the mixture firmly into the bottom of a 9-inch springform pan.
Bake for 8-10 minutes, or until lightly golden. Let cool completely.
In a medium saucepan, bring 4 cups of apple cider to a boil over medium-high heat.
Reduce the heat to medium and simmer for approximately 30-45 minutes, or until the cider has reduced to about ½ cup. It should be thick and syrupy. Let cool completely.
In a large bowl, beat the softened cream cheese with an electric mixer until smooth and creamy.
Gradually add the sugar and continue beating until well combined.
Beat in the eggs one at a time, mixing well after each addition. Be careful not to overmix.
Stir in the ½ cup of apple cider reduction, flour, vanilla extract, cinnamon, and nutmeg. Mix until just combined.
Pour the cheesecake filling over the cooled graham cracker crust.
Wrap the bottom of the springform pan tightly with aluminum foil.
Place the wrapped springform pan in a larger roasting pan.
Carefully pour hot water into the roasting pan until it reaches about halfway up the sides of the springform pan.
Bake in the preheated oven for 55-70 minutes, or until the edges are set but the center still has a slight jiggle.
Turn off the oven and let the cheesecake cool in the oven with the door slightly ajar for 1 hour.
Remove the cheesecake from the water bath and let it cool completely on a wire rack.
Cover the cheesecake with plastic wrap and refrigerate for at least 4 hours, or preferably overnight.
In a small saucepan, combine the remaining ½ cup of apple cider reduction, heavy cream, and butter.
Cook over medium heat, stirring constantly, until the butter is melted and the mixture is smooth and slightly thickened, about 2-3 minutes.
Remove from heat and stir in the sea salt. Let cool slightly.
In a small bowl, toss the thinly sliced apples with lemon juice.
Remove the cheesecake from the springform pan.
Drizzle the apple cider caramel topping over the cheesecake.
Arrange the apple slices on top of the caramel, if desired.
Slice and serve!