Combine graham cracker crumbs, melted butter, and brown sugar in a mixing bowl. Stir until the mixture resembles wet sand. Press the mixture firmly into the bottom of a 9-inch springform pan to form an even layer. Set aside.

In a large bowl, beat the softened cream cheese until smooth. Add the granulated sugar and continue mixing until the texture becomes silky. Blend in the sour cream and vanilla extract until combined. Add the eggs one at a time, mixing on low speed after each addition to prevent overbeating.

Pour the cheesecake filling over the prepared crust. Smooth the top with a spatula to create an even surface.

Place the springform pan inside a larger roasting pan. Fill the roasting pan with hot water until it reaches halfway up the sides of the springform pan.

Bake at 325°F (163°C) for 60 to 70 minutes. The center should still jiggle slightly when gently shaken. Turn off the oven, crack the door open, and let the cheesecake cool inside the oven for 1 hour.

While the cheesecake bakes and cools, toss the diced apples with lemon juice in a large bowl. Add brown sugar, cinnamon, nutmeg, flour, oats, and cubed butter. Use your fingertips to work the butter into the mixture until it resembles coarse crumbs.

Spread the apple crisp mixture evenly on a baking sheet. Bake at 350°F (175°C) for 20 minutes or until golden and fragrant. Let cool completely.

After cooling in the oven, refrigerate the cheesecake for at least 4 hours or overnight to fully set.

Once fully chilled, spoon the cooled apple crisp topping evenly over the cheesecake. Drizzle caramel sauce over the top just before serving.