For the Blueberry Filling:

1. In a medium saucepan, combine the fresh blueberries, sugar, water, and cornstarch.

2. Cook over medium heat, stirring frequently, until the mixture comes to a simmer and the blueberries begin to break down, about 5-7 minutes.

3. Continue cooking for another 2-3 minutes until the mixture thickens.

4. Remove from heat and allow the blueberry filling to cool while you prepare the other ingredients.

For the Cream Cheese Filling:

1. In a mixing bowl, beat the room temperature cream cheese and sugar together until smooth and creamy.

2. Add the lemon juice and vanilla extract and continue to mix until well combined.

3. Set aside until ready to assemble.

Assembling the Pastry Braid:

1. Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.

2. Roll out the puff pastry on a lightly floured surface into a rectangle (about 12×9 inches).

3. Spread the cream cheese filling down the center of the puff pastry, leaving about 2 inches on each side.

4. Spoon the blueberry filling over the cream cheese layer.

5. Cut diagonal slits on both sides of the pastry to create strips (about 1-inch wide).

6. Carefully fold the strips over the blueberry filling, alternating sides to form a braid. Pinch the ends together to seal.

7. Beat the egg with 1 tablespoon of water to make an egg wash. Brush the top of the braided pastry with the egg wash to give it a golden, glossy finish.

8. Bake for 25-30 minutes, or until the pastry is golden and puffed.

For the Lemon Icing:

1. While the pastry is baking, whisk together the powdered sugar, heavy cream, lemon juice, and vanilla extract in a small bowl until smooth.

2. Once the pastry is done baking and has cooled slightly, drizzle the lemon icing over the top.