Divide the prepared dough evenly into 6 equal portions on a lightly floured surface; shape each piece into a ball. Roll each ball into a 6-inch circle. Combine egg and water with a whisk in a small bowl. Brush edge of each circle with egg mixture; reserve remaining egg mixture.
Place 1/6 of shrimp mixture on half of each circle. Fold the dough over shrimp mixture until edges almost meet. Bring the bottom edge over top edge; crimp edges of the dough with fingers to form a rim. Place calzones on a baking sheet sprinkled with cornmeal. Brush tops with the reserved egg mixture. Bake calzones at 450° for 12 minutes or until golden brown.