Mix graham cracker crumbs, sugar, and melted butter until the mixture looks like wet sand. Press it firmly into lined muffin cups to create an even base. A flat-bottomed glass helps pack the crust tightly.
Beat the softened cream cheese until smooth and creamy. Add sugar, eggs, vanilla, and sour cream, mixing just until combined. Overmixing can cause cracks, so keep it gentle.
Spoon the cheesecake mixture over the crusts, filling each liner about three-quarters full. This leaves space for the apple and crumble topping without overflow.
Toss diced apples with brown sugar and cinnamon until evenly coated. The sugar draws out moisture while baking, creating a soft and flavorful apple layer.
Combine flour, oats, brown sugar, and cold butter. Use your fingers to crumble the mixture until it forms pea-sized clumps. This creates a crisp, golden topping.
Spoon apples over the cheesecake filling, then sprinkle with crumble topping. Bake until the centers are just set and the tops are lightly golden.
Let the cheesecakes cool at room temperature, then refrigerate for at least two hours. Chilling helps them firm up and improves the overall texture.