In a large mixing bowl, whisk together 4 cups of all-purpose flour, 1/4 cup of sugar, 2 teaspoons of instant yeast, and 1 teaspoon of salt. Gradually add 1 cup of warm milk and a large egg, then mix in 1/4 cup of softened butter until the dough is soft and slightly sticky.

Transfer the dough onto a floured surface and knead for about 8-10 minutes until smooth and elastic. Let rise for 1 hour in a greased bowl covered with a kitchen towel.

Mix 8 ounces of cream cheese, 1/4 cup of powdered sugar, 1 teaspoon of vanilla extract, and 1 egg yolk in a bowl until smooth. Refrigerate the mixture.

In a saucepan, combine 2 cups of blueberries, 1/4 cup of sugar, and the juice of half a lemon. Cook for about 5 minutes until juices release. Mix 1 tablespoon of cornstarch with 1 tablespoon of water and add to the saucepan. Cook for another 2 minutes until thickened.

Punch down risen dough, divide into 10-12 equal pieces, and shape into smooth balls. Flatten slightly and create indents in the center.

Fill the indent with cheesecake filling, topping with a dollop of blueberry compote, being careful not to overfill.

Preheat the oven to 180°C (350°F), brush buns' edges with beaten egg, and bake for 18-22 minutes until golden.

Let the buns cool on a wire rack for about 10 minutes before serving warm, optionally dusting with powdered sugar.