Preheat the oven to 325°F. Grease a 9-inch springform pan.
In a medium bowl, combine graham cracker crumbs, melted butter, and 1/4 cup sugar. Mix until well combined. Press the mixture firmly into the bottom of the prepared springform pan to form the crust.
In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth and creamy. Gradually add 1 cup sugar and vanilla extract, mixing until well combined.
Add the eggs one at a time, mixing on low speed until just combined after each addition. Stir in the sour cream until smooth.
In a separate bowl, toss the diced apples with cinnamon and nutmeg. Gently fold the spiced apples into the cream cheese mixture.
Pour the cheesecake batter over the crust in the springform pan. Bake for 50-60 minutes, or until the center is set but still slightly jiggly.
Turn off the oven and crack the door, allowing the cheesecake to cool in the oven for 1 hour.
Remove the cheesecake from the oven and let it cool to room temperature. Once cooled, refrigerate for at least 4 hours or overnight.
Before serving, drizzle caramel sauce over the top of the cheesecake. Slice and enjoy!