In a medium bowl, beat together the softened cream cheese, granulated sugar, and vanilla extract until smooth and creamy, using a hand mixer or stand mixer. Set aside 2 tablespoons of this mixture in a small bowl for the glaze. Keep the remaining filling refrigerated until needed.

Let the puff pastry sheets sit at room temperature for about 40 minutes, but handle them while still cool to the touch. Preheat your oven to 425°F and allow it to heat for 15 to 20 minutes before baking.

On a lightly floured surface, roll each pastry sheet into an 8- to 10-inch square. Cut each square into 4 smaller squares (about 4 to 5 inches each). Fold each small square in half to form a triangle.

Using a sharp knife, cut a slit about 1/2 inch from the folded edge, starting from the folded side and stopping about 1/2 inch from the point of the triangle. Unfold the square. Fold one cut corner over to the opposite inner cut corner, then repeat with the other cut corner to form a twisted pastry shell.

In a small bowl, whisk the egg with 1 teaspoon water to make an egg wash. Brush the egg wash only over the tops of the pastry twists, being careful not to let it drip onto the cut sides. Spoon or pipe the reserved cream cheese filling into the center of each pastry. Top generously with mixed berries.

Bake in the preheated oven until the pastries are puffed and golden brown, about 10 to 15 minutes. Let cool on the baking sheet for 5 minutes, then transfer to a wire rack.

To the reserved 2 tablespoons of cream cheese mixture, add a small amount of heavy whipping cream (about 1 to 2 teaspoons) and stir until smooth and drizzle-able. Drizzle the glaze over the cooled pastries, then dust with confectioners' sugar. Serve at room temperature.