Preheat the oven to 350°F (175°C) and line a muffin pan with paper liners.
Make the streusel by mixing flour, oats, brown sugar, cinnamon, and nutmeg. Stir in melted butter until crumbly.
Combine brown sugar and cinnamon for the cinnamon-sugar mixture.
Toss diced apples with granulated sugar and cinnamon until evenly coated.
In a large bowl, beat butter, sugar, and vanilla until light. Add eggs one at a time.
Mix flour, baking powder, and salt together. Gradually add to the wet ingredients, alternating with milk. Mix until just combined.
In another bowl, beat cream cheese, sugar, flour, vanilla, and egg until smooth.
To assemble the Apple Crisp Cheesecake Muffins, add a spoonful of muffin batter to each liner. Top with apples and a sprinkle of cinnamon sugar.
Add a spoonful of cheesecake filling, followed by more apples and another sprinkle of cinnamon sugar.
Cover with additional muffin batter until liners are about three-quarters full.
Sprinkle generously with streusel 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.
Mix icing ingredients until smooth and drizzle over completely cooled muffins.