Preheat your oven to 400°F (200°C).
Thaw the puff pastry sheets on a floured surface for about 30 minutes.
Roll out the puff pastry sheets slightly thinner and then cut them into squares (about 3x3 inches).
In a bowl, mix the shredded mozzarella cheese and pesto until well combined.
Place a tablespoon of the cheese-pesto mixture in the center of each pastry square.
Fold the pastry squares into triangles and seal the edges with a fork or pinch them closed.
Brush the tops with beaten egg for a golden finish.
Bake for 15-20 minutes or until golden brown and puffed.
Allow to cool for a few minutes before serving warm.