Preheat your oven to 350°F (175°C). In a medium bowl, mix the graham cracker crumbs and 1/3 cup of sugar. Stir in the melted butter until the mixture is evenly moist and resembles wet sand.
Firmly press the crumb mixture into the bottom and about halfway up the sides of a 9-inch springform pan. Use the bottom of a flat glass or measuring cup to create an even, compact crust. Bake for 10 minutes, then set aside to cool.
In a large mixing bowl, beat the softened cream cheese, 1 cup of sugar, and vanilla extract with an electric mixer on medium speed until the mixture is completely smooth and creamy, about 2-3 minutes. Scrape down the sides of the bowl as needed.
Add the eggs one at a time, beating on low speed just until each egg is incorporated after each addition. Be careful not to overmix. Gently fold in the 1/2 cup of caramel sauce, chopped apples, and cinnamon with a spatula until just combined.
Pour the cheesecake filling over the cooled crust and spread it evenly. Tap the pan gently on the counter a few times to release any large air bubbles.
Bake for 45-55 minutes, or until the edges are set and the center still has a slight jiggle when the pan is gently shaken. The center should not be liquid.
Turn off the oven, crack the oven door open with a wooden spoon, and let the cheesecake cool inside the oven for 1 hour. This gradual cooling helps prevent cracking.
Remove the cheesecake from the oven and run a thin knife around the edge of the pan to loosen it. Let it cool completely at room temperature, then refrigerate for at least 4 hours, or preferably overnight, before serving. Drizzle with additional caramel sauce just before serving.