Line two rimmed baking sheets with parchment paper and set aside. Cut two sheets of thawed puff pastry into 4-inch-by-4-inch squares and keep refrigerated until ready to use.
To assemble a pastry, take one square, leave a bit (say 1/4-inch) border, then layer 1/6 of the prosciutto and the cheese in the center. Brush the edide with egg wash, top with a second puff pastry square then cut a slit in the center. Repeat to make six pastries. Place in the refrigerator to chill about 15 to 20 minutes (pastries can be made and refrigerated up to 1 day ahead at this point) while you heat the oven.
Meanwhile, heat the oven to 425°F and arrange a rack in the middle. Remove pastries from the refrigerator and brush pastries with the remainingegg wash. Arrange the pastries on the baking sheets then bake, rotating the sheets once, until the pastries are golden brown and all the cheese is melted, about 20 to 25 minutes.