In a large mixing bowl, combine 4 cups of all-purpose flour, 1 cup of warm whole milk, 1 large egg, 2 teaspoons of instant yeast, 1/4 cup granulated sugar, 1/4 cup vanilla sugar, and 1 teaspoon salt. Mix until well incorporated, knead on a floured surface for 8-10 minutes until smooth and elastic. Place in a greased bowl, cover, and let rise in a warm spot for 1 hour, until doubled.

Peel, core, and dice 2 cups of apples. Melt 2 tablespoons of unsalted butter in a skillet over medium heat. Add the diced apples, 1/4 cup brown sugar, and 1 teaspoon of cinnamon; cook until softened, about 5-7 minutes. Combine 2 tablespoons of cornstarch with 2 tablespoons of water and stir into the skillet. Cook until glossy and remove from heat to cool completely.

In a mixing bowl, beat together 8 ounces of cream cheese, 1/4 cup granulated sugar, and 1 tablespoon of vanilla sugar until smooth, about 3-5 minutes. Set aside for assembly.

After the dough has risen, punch it down, divide into 9 portions, and roll into balls. Rest for 15 minutes, then press to create shallow indentations to hold the filling.

Preheat oven to 180°C (350°F). Spoon cheesecake filling and cooled apple mixture into each dough indentation. Mix 1 cup flour, 1/2 cup cold butter, and 1/4 cup brown sugar for the crumble topping and sprinkle over each filled bun.

Place assembled buns on a parchment-lined baking sheet, bake for 20-25 minutes until golden brown. They'll be done when puffy and aromatic.

Allow baked buns to cool for 10 minutes. Whisk 1 cup powdered sugar with milk until smooth and drizzle over buns. Serve warm for best flavor.