Preheat your oven to 325°F (163°C).
Combine graham cracker crumbs, ¼ cup sugar, and melted butter in a bowl. Press the mixture into the bottom of a springform pan and slightly up the sides. Bake for 10 minutes. Let cool.
In a skillet, cook the sliced apples with brown sugar, cinnamon, and 1 tablespoon butter over medium heat until soft and slightly caramelized. Let cool.
In a large bowl, beat the cream cheese until smooth. Add sugar and vanilla, then beat in the eggs one at a time until well combined.
Pour half the cheesecake batter into the crust. Add a layer of apples, then pour the remaining batter over the top. Gently swirl the caramel sauce into the top layer with a knife.
Bake for 55–60 minutes or until the center is almost set. Let the cheesecake cool completely, then refrigerate for at least 4 hours or overnight.
Before serving, drizzle with extra caramel sauce and top with additional apple slices if desired.