In a small bowl, combine warm milk, active dry yeast, and granulated sugar. Allow to sit for about 5–10 minutes until frothy.

In a large mixing bowl, combine 2½ cups all-purpose flour and salt. Add the yeast mixture, large egg, and softened unsalted butter. Mix until a dough forms.

Knead the dough on a floured surface for about 5–7 minutes until smooth and elastic.

Place the dough in a greased bowl, cover with a clean cloth, and let rise in a warm place until doubled in size, about 1 hour.

In a medium bowl, mix diced apples, brown sugar, cinnamon, nutmeg, and cornstarch. Set aside.

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

In a separate bowl, mix ¼ cup all-purpose flour, 2 tablespoons brown sugar, and diced cold butter until crumbly.

Once risen, punch down the dough and divide it into equal pieces. Shape each piece into a round and press in the center to create an indention.

Spoon the cheesecake filling into the center, then top with the apple mixture. Sprinkle the crumble on top.

Place filled buns on a baking tray lined with parchment paper, cover, and let them rise again for 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 extract until smooth.

Once baked, drizzle the glaze over the warm buns and serve either warm or cooled.