In a large mixing bowl, combine warm milk, active dry yeast, and granulated sugar. Let it sit for about 5 minutes until frothy.

Mix in all-purpose flour, salt, egg, and softened unsalted butter. Knead the dough for 8-10 minutes until smooth, then cover and let rise in a warm spot for about 1 hour.

While the dough rises, prepare the apple filling by cooking diced apples, brown sugar, cinnamon, nutmeg, and unsalted butter in a saucepan for 5-7 minutes.

In a medium bowl, beat together softened cream cheese, powdered sugar, egg yolk, and vanilla extract until creamy.

Create the crumble topping by mixing flour and brown sugar, then cutting in cold butter until mixture resembles coarse crumbs.

Once the dough has risen, punch it down and divide into 12 pieces. Roll each piece into a round shape and create a well in the center.

Spoon cheesecake filling into the well, followed by apple filling, and top with crumble mixture.

Arrange filled buns on a baking sheet lined with parchment paper, cover, and allow to rise for another 30 minutes.

Preheat the oven to 350°F (175°C). Bake the buns for 20-25 minutes until golden brown.

In a small bowl, whisk together powdered sugar, milk, and vanilla for the glaze. Drizzle over the warm buns.