Preheat your oven to 325°F (160°C).
In a bowl, combine the graham cracker crumbs, 1/4 cup of sugar, and melted butter. Mix until the crumbs are evenly coated.
Press the mixture into the bottom of your 9-inch springform pan. Ensure it's evenly distributed and firmly packed.
Bake the crust for 10 minutes in the preheated oven, then remove and let it cool while you prepare the filling.
In a large mixing bowl, beat the softened cream cheese until it's smooth and creamy.
Gradually add 1 cup of sugar and continue to beat until well combined.
Beat in the eggs, one at a time, ensuring each egg is fully incorporated before adding the next.
Mix in the vanilla extract.
Pour the cream cheese filling over the baked graham cracker crust.
Place the springform pan on a large piece of aluminum foil and wrap it around the sides to prevent any water from the water bath leaking into the pan.
Create a water bath by placing the wrapped springform pan on a baking sheet and filling the sheet with hot water until it reaches halfway up the side of the pan.
Bake the cheesecake for 50-60 minutes or until the edges are set, but the center is slightly wobbly.
Turn off the oven, crack the oven door open, and let the cheesecake cool for 1 hour.
Remove the cheesecake from the water bath and refrigerate it for at least 4 hours or overnight to set.
In a saucepan, combine diced apples and lemon juice to prevent browning.
In a separate bowl, mix 1/2 cup of sugar, cinnamon, and cornstarch.
Add the sugar mixture to the apples and cook over medium heat until the apples are soft and the mixture thickens. Set aside to cool.
In a saucepan, melt 1 cup of sugar over medium-high heat, stirring constantly.
Once the sugar has melted and turned a deep amber color, add the butter and stir until it's fully melted and incorporated.
Carefully pour in the heavy cream while continuing to stir. Be cautious as the mixture may bubble up.
Remove the saucepan from heat and stir in the vanilla extract.
Spread the cooled apple topping over the chilled cheesecake.
Drizzle the caramel sauce over the apple topping, and let it drip down the sides for an enticing look.
Slice and enjoy your Caramel Apple Cheesecake!