Preheat the oven to 325°F. In a bowl, combine the graham cracker crumbs, dark brown sugar, cinnamon, nutmeg, and melted butter until it looks like wet sand. Press firmly into the bottom of a springform pan and bake for 10 minutes. Set aside to cool.

In a separate bowl, toss the diced apples with the granulated sugar and cinnamon. Let them sit for 30 minutes so the sugar draws some of the water out of the apples.

To make the streusel, combine the flour and dark brown sugar, then work in the room temperature butter with your fingers or a fork until it forms coarse, crumbly clusters. Set aside.

For the cheesecake filling, beat the cream cheese and granulated sugar until smooth and creamy. Mix in the sour cream, cornstarch, and vanilla. Add the eggs one at a time on low speed, mixing just until combined after each so you don't whip in too much air.

Pour the filling over the cooled crust and smooth the top.

Strain any liquid from the apples, then gently spoon them in an even layer over the filling.

Sprinkle the streusel evenly over the apples.

Fill a large, deep baking pan with boiling water and place it on the lower rack of the oven. Set the cheesecake on the rack above it.

Bake at 325°F for 1 hour 20 minutes to 1 hour 40 minutes, until the edges are set and the center jiggles slightly but doesn't ripple like liquid.

Turn off the oven, crack the door, and let the cheesecake cool inside for 1 hour. Then cool completely at room temperature and refrigerate for at least 4 hours or overnight before slicing.