In a mixing bowl, combine warm milk, active dry yeast, and granulated sugar, letting it sit for about 5-10 minutes until foamy.

Stir in all-purpose flour, salt, a large egg, and softened butter. Knead the dough for 8-10 minutes until smooth and elastic.

Cover with a clean kitchen towel and let it rise in a warm place for about 1 hour or until doubled in size.

Peel and dice your apples. In a skillet, melt some butter over medium heat and add the diced apples, brown sugar, cinnamon, nutmeg, and cornstarch.

Cook for approximately 5-7 minutes until the apples are tender, then remove from heat and let cool.

In a mixing bowl, blend cream cheese, powdered sugar, egg yolk, and vanilla extract until creamy and smooth.

In a separate bowl, combine cold butter, granulated sugar, and all-purpose flour until crumbly.

Once the dough has risen, punch it down and divide into equal pieces. Roll each piece into a circle, press the center down, and add the cooled apple mixture and cheesecake filling.

Fold the edges to seal and place seam side down on a parchment-lined baking sheet. Sprinkle with crumble topping.

Cover with a kitchen towel and allow to rise again for about 30 minutes.

Preheat oven to 350°F (175°C) and bake for 20-25 minutes until golden brown.

Whisk together powdered sugar, milk, and vanilla extract for the glaze.

After baking, let the buns cool for about 10 minutes and drizzle with sweet glaze.