Preheat oven to 400 degrees F (200 degrees C). Place both sheets of puff pastry on a large baking sheet, and pinch together in the center to make one large sheet. Bake for 15 minutes.
Meanwhile, heat oil over medium heat in a small skillet. Cook green onion, onion, garlic, tomatoes, and rosemary in oil until the onions are soft, about 5 minutes.
Remove puff pastry from oven, and top with mozzarella and Gorgonzola cheeses and onion and garlic mixture. Return to the oven, and bake until cheese is melted, about 10 minutes. Cut into 2 inch squares to serve.