Position a rack in the center of the oven and heat the oven to 400°F. Line a rimmed baking sheet with parchment. Whisk the egg yolk with 1/2 tsp. water.
Lightly dust a work surface with flour and gently unfold the pastry sheet. Roll out the pastry, eliminating the creases, to a 10- by 14-inch rectangle. Cut the rectangle in half lengthwise to make two 5- by 14-inch rectangles, and if the edges are uneven or ragged, trim them. Transfer both pastries to the baking sheet. With the tines of a fork, press a 1/4-inch border around the edge of the pastry. Brush the egg mixture along the border (you will not need all of it). Prick the rest of the pastry all over with the fork to keep the pastry from puffing too much. Bake both pastry rectangles until firm and golden, about 12 minutes. Remove the pastry from the oven and increase the temperature to 475°F.
Let the pastry rectangles cool slightly and press them gently to flatten any large air pockets. Scatter a thin layer of the sun-dried tomatoes on both rectangles. Scatter the Fontina over the top. Place the prosciutto strips on top of the Fontina, either draping them in a random pattern or arranging them evenly. Sprinkle the top with the Parmigiano. Bake until the cheese has melted, about 5 minutes. Let cool for a few minutes, then cut into strips or small squares to serve.
nutrition information (per serving):
based on eight servings;
Photo: Scott Phillips