In a medium bowl, combine cheeses, egg, green onion and pepper; set aside.
On a lightly floured surface, roll out half the puff pastry to a 10 inch square. With a sharp knife, cut pastry into 9 even squares, repeat with other half of puff pastry.
Working with one square at a time, place a spoonful of the cheese mixture in the middle of each pastry square; brush edges very lightly with water, then fold one corner over to meet the opposite corner, forming a triangle.
Press edges together to seal, then crimp firmly shut with the tines of a fork.
Place triangles on baking sheet; brush the tops with the second beaten egg.
Bake for 13 to 15 minutes or until the tops are golden and the bottoms are nicely browned.