Preheat oven to 350 degrees F. Roll out both sheets of pastry dough to 1/2-inch thickness.
Lay 1 sheet out on a prepared cookie sheet, brush with butter. Mix cheeses, egg, and basil together. Add salt and pepper to taste. Spread cheese mixture evenly over pastry. Top with second pastry sheet. Brush with butter and sprinkle with some more parmesan if you wish.
Bake until golden and puffy. Let cool and cut into 1-inch squares.