Prepare the dough - Combine 400g flour, 200ml lukewarm milk, 1 egg, 65g room temperature butter, 10g dry yeast, 60g sugar, 1 packet of vanilla sugar, and a pinch of salt in a large bowl. Knead thoroughly until you achieve a soft, elastic dough. Cover the bowl with a clean kitchen towel and place it in a warm spot to rise for 1 hour, or until the dough has doubled in size.

Make the apple filling - Peel 2 apples and cut them into small, uniform cubes. Heat a pan over medium heat and melt 1 tablespoon of butter. Add the apple cubes, 2 tablespoons of brown sugar, and 1 teaspoon of cinnamon. Cook the mixture, stirring occasionally, until the apples release their juices and then reabsorb them, about 5-7 minutes. In a small bowl, dissolve 1 teaspoon of cornstarch in 50ml of water, then pour this slurry into the pan. Cook for an additional 2 minutes, stirring constantly, until the mixture thickens to a jam-like consistency. Remove from heat and allow to cool completely.

Prepare the cream cheese filling - In a medium bowl, combine 200g cream cheese, 2 tablespoons of sugar, and 1 packet of vanilla sugar. Mix until smooth and well incorporated. Set aside at room temperature to ensure easy spreading.

Shape the dough - Once the dough has doubled in size, punch it down to release any air bubbles. Divide it into 9 equal portions and roll each portion into a smooth ball. Place the balls on a baking sheet lined with parchment paper, leaving enough space between each for expansion. Allow them to rest for 15 minutes.

Make the crumble topping - In a small bowl, combine 20g butter, 1 tablespoon sugar, and 60g flour. Use your fingertips to work the ingredients together until the mixture resembles coarse crumbs with a sandy texture. Set aside.

Fill the buns - Dip a glass in flour and use it to press a deep indentation into the center of each dough ball, creating a well while maintaining a thick border around the edges. Brush the exposed dough edges with egg yolk. Spoon a portion of the cream cheese filling into each well, then top with a tablespoon of the apple filling. Sprinkle the crumble topping generously over each filled bun.

Bake the buns - Preheat your oven to 180°C (356°F) with top and bottom heat. Bake the filled buns for 20-25 minutes, or until they are golden brown around the edges and the dough is fully cooked. Transfer to a wire rack to cool slightly.

Apply the icing - While the buns are cooling, prepare the icing by mixing 150g powdered sugar with 2 tablespoons of milk until smooth. Once the buns have cooled but are still slightly warm, drizzle the icing over the tops in a decorative pattern.