Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper.
Place the marinara sauce in a medium saucepan over medium heat and cook until reduced to a thick, jam-like consistency, about 30 minutes. There should be 1 1/2 to 2 cups of reduced sauce. Let the sauce cool to room temperature, about 30 minutes. Stir in the mozzarella cheese and prosciutto.
Meanwhile, place 1 piece of dough on a work surface. Roll the dough out gently until you can cut an 8 1/2 by 9 1/2-inch rectangle. Press the scraps into a small rectangle and roll it out to the same thickness as the other rectangle. Cut 3 rectangles from the large rectangle and 1 rectangle from the small rectangle. Each should measure 8 1/2 by 3 inches. Continue rolling and cutting the remaining pie dough.
To form the tarts, place the rectangles on a work surface. Brush each rectangle with egg wash. Place a large spoonful of the marinara mixture in the middle of the bottom half of the rectangle. Fold the dough in half over the marinara mixture to make a 3 by 4-inch rectangle. Press the edges to seal. Using a scalloped ravioli cutter, trim the rectangles to make a decorative edge. Place the tarts on the baking sheets. Brush with egg wash and generously sprinkle with cheese. Bake until golden, about 20 to 25 minutes.