Preheat your oven to 400°F. Line a baking sheet with parchment paper.
On a lightly floured surface, roll out each sheet of puff pastry to smooth out creases. Cut each sheet into 4 equal squares.
In a mixing bowl, combine the softened cream cheese, powdered sugar, cocoa powder, and vanilla extract. Mix until smooth and well combined.
Place a tablespoon of the chocolate cream cheese mixture in the center of each puff pastry square. Sprinkle a few chocolate chips on top of the filling.
Fold the corners of each pastry square towards the center, pinching them together to seal. Brush the tops with the beaten egg.
Bake in the preheated oven for 15-20 minutes, or until golden brown and puffed. Remove from the oven and let cool slightly.
In a small bowl, mix the milk with the remaining powdered sugar to create a drizzle. Drizzle over the warm pastries before serving.