Prep the muffin tin: Line a 12-cup muffin tin with paper liners and preheat the oven to 325°F. This keeps the cheesecakes easy to remove once they chill.
Mix the crust: Stir together graham cracker crumbs, 3 tablespoons melted butter and 1 tablespoon sugar until it looks like wet sand. Press about a tablespoon into each liner and pack it down firmly with a spoon.
Bake the crust: Bake the crusts for 5 minutes until the edges look slightly golden. Set aside to cool while you make the filling.
Beat the cream cheese: Beat the softened cream cheese on medium speed until smooth, about 2 minutes, scraping the bowl once. Add 2/3 cup sugar and beat until fully combined.
Add eggs and vanilla: Add the eggs one at a time, mixing on low just until each is incorporated. Stir in the vanilla extract, keeping the mixing brief to avoid adding extra air.
Cook the apples: In a skillet over medium heat, melt 2 tablespoons butter and add the diced apples, 3 tablespoons brown sugar and 1/2 teaspoon cinnamon. Cook, stirring occasionally, until the juices thicken into a glaze, about 5 minutes, then remove from heat to cool completely.
Fill the crusts: Divide the cheesecake batter evenly among the crusts, filling each about three-quarters full. Spoon the cooled apple mixture over the top of each one.
Bake the cheesecakes: Bake at 325°F for 18 to 20 minutes, until the edges look set but the centers still jiggle slightly when the pan is nudged. Avoid opening the oven door during the first 15 minutes.
Cool and chill: Let the cheesecakes cool in the pan to room temperature, then refrigerate at least 4 hours or overnight to fully set.
Make the crumble: Mix oats, flour, remaining brown sugar, remaining cinnamon and nutmeg in a bowl, then cut in the cold cubed butter with your fingers until it forms coarse crumbs. Toast in a dry skillet over medium-low heat, stirring often, until golden and fragrant, about 4 minutes.
Top and serve: Remove the chilled cheesecakes from the liners and sprinkle the oat crumble over the apples just before serving so it stays crunchy.