In a large mixing bowl or stand mixer, combine the all-purpose flour, warmed whole milk, large egg, instant yeast, granulated and vanilla sugars, and a pinch of salt. Knead the dough for 5-10 minutes until smooth and elastic. Cover with a damp cloth and let rise in a warm spot for about 1 hour.

In a skillet over medium heat, add diced apples, butter, brown sugar, and ground cinnamon. Sauté until apples soften, about 5-7 minutes. Stir in cornstarch mixed with water and cook for another minute. Remove from heat and let cool completely.

Mix cream cheese with granulated sugar and remaining vanilla sugar in a medium bowl. Blend until smooth and creamy.

Once the dough has risen, punch it down gently, divide into 9 equal portions, and roll each into a ball. Rest for about 15 minutes on a floured surface.

Press a floured glass into each dough ball to create a deep well for the filling.

Brush the edges of each well with egg yolk. Fill each indentation with cheesecake mixture followed by apple filling, being careful not to overfill.

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

Preheat oven to 180°C (350°F). Transfer assembled buns to a parchment-lined baking sheet and bake for 20-25 minutes until golden brown.

Let the buns cool slightly on a wire rack. Whisk powdered sugar and milk to achieve smooth glaze consistency, then drizzle over warm buns.