Preheat your oven to 400°F (200°C) and line two large baking sheets with parchment paper. Ensure your puff pastry is fully thawed but still cold to the touch for the best flakiness.

In a medium bowl, beat the softened cream cheese, granulated sugar, and vanilla extract until smooth and creamy. Set the mixture aside.

Unfold the puff pastry sheets on a lightly floured surface and cut each sheet into four equal squares, making eight squares total. Transfer the squares to the prepared baking sheets, leaving a couple of inches of space between them.

Using a paring knife, lightly score a smaller square inside each pastry square, leaving about a 1/2-inch border. Be careful not to cut all the way through the dough; this helps the edges rise around the filling.

Spoon about 1.5 tablespoons of the cream cheese mixture into the center of each scored square, spreading it evenly within the inner border. Top the cream cheese generously with the fresh mixed berries, pressing them down slightly so they adhere.

In a small bowl, whisk together the egg and water to create an egg wash. Brush the exposed 1/2-inch borders of the puff pastry with the egg wash to ensure they bake to a beautiful golden brown.

Bake in the preheated oven for 18 to 20 minutes, or until the pastry edges are puffed, crisp, and deeply golden. Let the pastries cool on a wire rack for at least 10 minutes, then lightly dust with powdered sugar before serving warmly with a cup of coffee.