In a large mixing bowl, whisk together 4 cups of all-purpose flour, ½ cup of granulated sugar, 2 teaspoons of instant yeast, and 1 teaspoon of salt. Gently heat 1 cup of milk until warm, and add it to the dry ingredients along with 1 large egg and ½ cup of softened butter. Mix until combined, forming a soft dough.

Transfer the dough to a floured surface and knead for about 8-10 minutes until it becomes smooth and elastic. Place the kneaded dough into a greased bowl, cover it with a damp cloth, and allow it to rise in a warm area for about 1 hour, or until doubled in size.

In a medium bowl, beat together 8 oz of cream cheese, ¼ cup of powdered sugar, 1 teaspoon of vanilla extract, and 1 egg yolk until smooth and creamy. Set the filling in the refrigerator to chill while the dough continues its first rise.

In a saucepan over medium heat, combine 2 cups of blueberries, ¼ cup of sugar, and 1 tablespoon of lemon juice. Cook for about 5-7 minutes, stirring occasionally, until the blueberries start to burst. Mix 1 tablespoon of cornstarch with 2 tablespoons of water and add to the saucepan. Stir until thickened, about 2 minutes, then remove from heat.

After the dough has risen, punch it down to remove excess air. Divide it into 10-12 equal pieces and shape each piece into a ball. Make an indent in the center of each ball using your thumb.

Spoon about a tablespoon of the chilled cheesecake filling into the indent of each dough ball. Next, add a teaspoon of the blueberry compote on top. Sprinkle with crumble topping if desired, then pinch the dough around the filling to seal the buns.

Preheat your oven to 350°F (180°C). Prepare an egg wash by whisking one egg with a splash of water. Brush the tops of the filled buns with the egg wash to create a beautiful golden finish. Bake the buns for 18-22 minutes, or until they are golden brown.

Once the buns are baked to perfection, remove them from the oven and let them cool on a wire rack for about 10-15 minutes. Serve warm and enjoy!