Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.
On a lightly floured surface, gently roll the thawed sheet of puff pastry to about 9 × 10.5 inches.
Cut the pastry into 8 equal rectangles and place them on the prepared baking sheet, leaving a little space between each.
In a bowl, whisk together the cream cheese, powdered sugar, and vanilla extract until smooth.
Spoon the cream cheese mixture into a zip-top bag, squeeze the mixture toward one corner, and snip off the tip of that corner to make a piping hole.
Pipe the cream cheese mixture onto the center of each pastry rectangle, leaving a small border (about 1/4 inch) of exposed pastry around the edges.
In a small bowl, whisk the egg and 2 tablespoons water together until combined. Brush this egg wash onto the exposed pastry borders (avoid brushing over the filling).
Bake for 10–12 minutes, until the pastry is puffed and golden brown. Remove from the oven, let cool briefly, and serve fresh.