Preheat the oven to 325°F with a rack in the center. Line a standard 12-cup muffin pan with paper liners.
Stir the graham crumbs, granulated sugar, and cinnamon together. Add 4 tablespoons melted butter and mix until evenly moistened. Divide among the liners and press firmly into flat layers.
Bake the crusts for 5 minutes, then place the pan on a rack to cool while preparing the toppings and filling.
Combine the flour, oats, brown sugar, cinnamon, nutmeg, and salt. Stir in 4 tablespoons melted butter with a fork until coarse crumbs form. Refrigerate until assembly.
Beat the cream cheese on low speed until smooth. Mix in the sugar and flour, followed by the sour cream and vanilla. Add the eggs one at a time on low speed, mixing only until combined.
Toss the diced apples with lemon juice, brown sugar, cinnamon, nutmeg, and cornstarch until evenly coated.
Divide the cheesecake batter evenly over the crusts. Spoon the apples on top and gently press them into the batter. Sprinkle generously with the cold oat streusel.
Bake for 24 to 28 minutes, until the edges are set, the streusel is lightly golden, and the centers still wobble slightly when the pan is nudged.
Cool in the pan for 30 minutes, then transfer the cheesecakes to a rack. Once at room temperature, refrigerate for at least 3 hours.
Drizzle the chilled mini cheesecakes with caramel just before serving. Keep refrigerated until close to serving time.