Preheat the oven to 350°F. Line a standard muffin pan with paper liners.

Combine the graham cracker crumbs, sugar, and melted butter in a bowl until it resembles wet sand. Spoon a tablespoon of the mixture into the prepared muffin tins and firmly press down. Bake in the preheated oven for 6 minutes.

Using the same bowl, combine the crumb topping ingredients and cut the cold butter until coarse crumbs form. Keep chilled until ready to use.

Stir together diced apples, sugars, flour, lemon juice, cinnamon, nutmeg, and vanilla until evenly coated.

Using a handheld mixer or stand mixer fitted with the paddle attachment, beat the cream cheese and sugar on high for 2 minutes until smooth. Mix in sour cream, cornstarch, vanilla, and salt until creamy. Add eggs one at a time on low speed until just combined.

Divide cheesecake filling among liners, filling ¾ full. Divide apple filling evenly on top, then sprinkle with the crumble. Gently press it down.

Place a roasting pan or casserole dish with hot water on the lower oven rack. Bake for 20 minutes.

Cool on the counter for 30 minutes, then refrigerate at least 2 hours to fully set before removing liners. Top and serve chilled.