Prepare the Dough — In a large mixing bowl, whisk together the flour, granulated sugar, instant yeast, and salt until evenly combined. Add the warm milk, egg, and softened butter, mixing until a soft dough forms. Knead the dough for 8 to 10 minutes until smooth, elastic, and slightly tacky. Transfer the dough to a lightly greased bowl, cover, and allow it to rise for approximately 1 hour, or until doubled in size.
Make the Vanilla Cheesecake Filling — In a separate bowl, beat the cream cheese, powdered sugar, vanilla extract, and egg yolk until completely smooth and creamy. Cover and refrigerate until ready to use to help the filling maintain its shape during baking.
Prepare the Blueberry Compote — Combine the blueberries, granulated sugar, and lemon juice in a small saucepan set over medium heat. Simmer for about 5 minutes, stirring occasionally, until the berries release their juices. Stir in the cornstarch slurry and continue cooking until the mixture thickens. Remove from heat and allow to cool completely.
Prepare the Crumble Topping — In a bowl, rub the cold cubed butter into the flour and granulated sugar using your fingertips until the mixture resembles coarse crumbs. Refrigerate until needed to keep the crumble firm.
Shape the Buns — Punch down the risen dough and divide it into 10 to 12 equal portions. Shape each portion into a smooth ball and place on a parchment-lined baking tray. Gently flatten each bun and create a shallow indentation in the center using your fingers or the back of a spoon.
Fill and Assemble — Spoon the chilled cheesecake filling into the center of each bun, followed by a small amount of blueberry compote. Sprinkle the crumble topping around the edges of the buns, avoiding the center filling.
Bake the Buns — Preheat the oven to 180°C (350°F). Brush the exposed dough edges with the prepared egg wash. Bake for 18 to 22 minutes, or until the buns are golden brown and set.
Cool and Serve — Allow the buns to cool slightly before serving. Enjoy warm, optionally finished with a light dusting of powdered sugar.