Preheat the oven to 350°F (175°C) and line a muffin pan with paper liners.
Prepare the crisp topping by combining flour, oats, brown sugar, cinnamon, and nutmeg. Stir in melted butter until crumbly. Set aside.
Mix the brown sugar and cinnamon for the cinnamon sugar mixture.
Toss diced apples with granulated sugar and cinnamon until evenly coated.
In a bowl, whisk together flour, baking powder, and salt.
In another bowl, beat butter, sugar, and vanilla until light and fluffy. Add eggs one at a time.
Gradually add the dry ingredients, alternating with the milk, mixing just until combined.
For the cheesecake filling, beat cream cheese, sugar, flour, vanilla, and egg until smooth.
Assemble the Apple Crisp Cheesecake Muffins:
Spoon about one heaping tablespoon of muffin batter into each liner.
Add diced apples.
Sprinkle with cinnamon sugar.
Add a generous spoonful of cheesecake filling.
Top with more apples and another sprinkle of cinnamon sugar.
Cover with additional muffin batter until liners are about three-quarters full.
Finish generously with the crisp topping.
Bake for 23–28 minutes, or until a toothpick inserted into the muffin portion comes out clean.
Cool in the pan for 5 minutes before transferring to a wire rack.
Stir together powdered sugar, milk, and vanilla until smooth. Drizzle over completely cooled muffins.