In a large mixing bowl or stand mixer, combine all-purpose flour, warm milk, egg, instant yeast, granulated sugar, vanilla sugar, and salt. Mix until well-combined, then knead the dough for 5–10 minutes until smooth.

Cover the bowl with a damp cloth or plastic wrap and place it in a warm spot to rise for about 1 hour, or until doubled in size.

Prepare the apple filling by slicing apples into small pieces. In a skillet, melt a tablespoon of butter and sauté the diced apples with brown sugar and cinnamon for about 5–7 minutes. Make a cornstarch slurry, mix it in, and cook until thickened. Set aside to cool.

In a separate bowl, whisk together cream cheese, remaining brown sugar, and a dash of vanilla sugar until smooth and creamy.

After the first rise, punch the dough down and divide into 9 equal pieces. Roll each into a ball and let them rest for about 15 minutes.

Lightly flour a flat surface, and press down in the center of each dough ball to create a deep indentation.

Spoon cheesecake filling into each well, followed by a generous amount of the cooled apple mixture. Sprinkle cold crumble topping over each bun.

Preheat the oven to 180°C (350°F). Place the buns on a lined baking sheet and brush the exposed dough edges with egg wash. Bake for 20-25 minutes until golden brown.

Let the buns cool slightly on a wire rack, then prepare the glaze and drizzle it over the buns.