1. Make the Dough: In a large bowl, combine the flour, sugar, yeast, and salt. Add the warm milk, egg, and softened butter. Knead the mixture until it becomes smooth and elastic. Cover the dough and let it rise until it has doubled in size, approximately 1 hour.

2. Prepare the Cheesecake Filling: In a separate bowl, mix the cream cheese, powdered sugar, vanilla extract, and egg yolk until the mixture is smooth and creamy.

3. Create the Blueberry Topping: In a small saucepan, combine the blueberries, sugar, lemon juice, and cornstarch slurry. Cook over medium heat, stirring frequently, until the mixture has thickened. Remove from heat and let it cool.

4. Make the Streusel: In a bowl, combine the cold, cubed butter, sugar, and flour. Use your fingertips to work the ingredients together until you achieve a crumbly texture.

5. Assemble the Buns: Roll the dough out into a rectangle. Cut the dough into squares. Place a spoonful of the cheesecake filling in the center of each square, followed by a dollop of the blueberry topping. Fold the corners of the dough over the filling, or shape the buns as desired. Sprinkle the streusel over the top of the assembled buns.

6. Brush the Buns: In a small bowl, beat the egg and milk together. Brush the tops of the assembled buns with the egg wash mixture.

7. Bake the Buns: Preheat your oven to 375°F. Bake the Danish Carnival Buns with Vanilla Cheesecake for 20-25 minutes, or until they are golden brown in color.