In a large mixing bowl, combine all-purpose flour, warmed milk, egg, instant yeast, granulated sugar, and salt until well incorporated. Knead the mixture on a floured surface for 5-10 minutes until the dough becomes smooth and elastic. Place the dough in a greased bowl, cover it with a damp cloth, and let it rise in a warm area for about 1 hour, or until doubled in size.

While the dough is rising, prepare the apple filling. Peel and dice your apples, then sauté them in a skillet over medium heat with brown sugar and cinnamon for about 5-7 minutes, until slightly soft. Mix cornstarch with a splash of water and add it to the apples. Stir continuously until the mixture thickens; then remove from heat and allow it to cool completely.

In a medium bowl, whip together the cream cheese and sugar until smooth. Add the vanilla sugar and continue mixing until fully combined.

After the dough has risen, punch it down gently to release the air. Transfer it to a clean surface and divide it into 9 equal balls.

Take a floured glass or your fingers to gently press down in the center of each dough ball, creating a small bowl shape.

Using a pastry brush, lightly coat the edges of each indentation with the egg wash. Spoon a generous portion of the cheesecake mixture into each indentation, followed by the sautéed apple filling.

Prepare the crumble topping by mixing cold butter, sugar, and flour together until crumbly. Sprinkle the buttery crumbs generously over each filled bun.

Preheat your oven to 180°C (350°F). Once preheated, bake for 20-25 minutes, or until golden brown.

After baking, allow the buns to cool slightly on the tray. Prepare the glaze by whisking together powdered sugar and milk until smooth, then drizzle over the warm buns.