Prepare your oven and pan. Preheat your oven to 325°F (165°C). Line a standard 12-cup muffin tin with cupcake liners.
Make the graham cracker crust. In a medium bowl, combine graham cracker crumbs, sugar, melted butter, and cinnamon until the mixture resembles wet sand. Press about 2 tablespoons of the mixture into the bottom of each liner, using the bottom of a glass to compact it firmly.
Pre-bake the crusts for 5 minutes, then remove from the oven and allow to cool slightly while preparing the filling.
Prepare the cheesecake filling. In a large bowl, beat the softened cream cheese and sugar with an electric mixer until smooth and creamy, about 2 minutes. Add eggs one at a time, beating well after each addition. Mix in vanilla extract, flour, and sour cream until just combined. Be careful not to overmix.
Fill each muffin cup with the cheesecake batter, leaving about ¼ inch of space at the top for the apple mixture and crisp topping.
Prepare the apple topping. In a medium saucepan over medium heat, melt butter. Add diced apples, brown sugar, cinnamon, nutmeg, and lemon juice. Cook for 5-7 minutes, stirring occasionally, until apples are slightly softened but still hold their shape. Remove from heat and let cool slightly.
Make the crisp topping. In a medium bowl, combine flour, oats, brown sugar, salt, and cinnamon. Using your fingers or a pastry cutter, work the cold cubed butter into the dry ingredients until the mixture resembles coarse crumbs.
Assemble the mini cheesecakes. Spoon about 1 tablespoon of the apple mixture onto each cheesecake, then sprinkle a generous amount of crisp topping over the apples, pressing lightly to adhere.
Bake for 20-25 minutes until the centers are just set and the crisp topping is golden brown.
Cool completely in the pan on a wire rack for about 30 minutes, then transfer to the refrigerator to chill for at least 2 hours before serving.