In a large mixing bowl or stand mixer, combine all-purpose flour, warm milk, egg, instant yeast, granulated sugar, and salt. Mix until the dough begins to come together, then knead for 5-10 minutes until smooth and elastic. Gradually add softened unsalted butter, continuing to knead until the dough is silky. Cover with a damp cloth and let rise in a warm spot for about 1 hour, or until doubled in size.

While the dough is rising, prepare the apple filling by sautéing diced apples in a pan over medium heat with brown sugar and cinnamon. Cook for about 5-7 minutes, or until the apples are softened. Mix cornstarch with water, add it to the pan, and stir until thickened. Remove from heat and let cool completely.

In a separate bowl, whisk together the cream cheese, granulated sugar, and vanilla sugar until smooth and creamy. This rich filling contrasts beautifully with the apple filling.

Once the dough has risen, punch it down gently. Divide into 9 equal balls and let rest for about 15 minutes. Press down the center of each ball to create a well.

Preheat oven to 180°C (350°F). Brush the edges of each dough well with egg wash. Layer the cheesecake mixture in the center, followed by cooled apple filling, then top with crumble topping.

Place assembled buns on a parchment-lined baking sheet and bake for 20-25 minutes, or until golden brown and filling is set. Keep an eye on them towards the end of baking.

Remove from oven and let cool slightly. Prepare the glaze by whisking together powdered sugar and milk until smooth. Drizzle over warm buns before serving.