1 sheet frozen puff pastry (from a 17.3-ounce package, such as Pepperidge Farm), thawed in the refrigerator
2 tablespoons salted butter, melted
1 cup grated mozzarella (hard, not fresh)
3/4 cup grated Parmesan
2 tablespoons chopped fresh oregano
1 tablespoon chopped fresh basil
1 large egg
Warm marinara, for serving