Nearly any topping that works for a pizza makes a great calzone filling, with a few adjustments: Since soft melting cheeses shrink dramatically inside the calzone and give off moisture, I always include some other bulky ingredients like vegetables or meats. Just be sure to precook those other ingredients, or else they will give off moisture as well.
Take the dough out of the refrigerator, set it on a lightly oiled work surface, and divide into 4 equal pieces of about 7 oz. each. Roll each piece into a tight ball. Line a baking sheet with parchment and lightly oil it with olive oil or cooking spray. Set each ball at least an inch apart on the parchment. Lightly spray or brush the balls with olive oil and cover loosely with plastic wrap. Let the dough warm up and relax at room temperature for 1-1/2 to 2 hours.
Shape the dough:
Position a rack in the center of the oven and heat the oven to 500°F (a baking stone is optional). Fill a small bowl with bread flour, or semolina if using, and dust a clean work surface with a generous amount.
With floured hands, transfer one of the dough balls to the floured work surface. Sprinkle lightly with flour and press it with your fingertips into a round disk. With a rolling pin, roll the dough out into an oval or round shape about 3/16 inch thick and 9 inches across. Dust with flour as necessary to prevent sticking. If the dough resists rolling and springs back, let it rest for a few minutes and move on to the next dough ball. Roll out the remaining three dough balls.
Fill and bake the calzones:
Brush the edge of a dough round with cool water to make a damp band about 1/2 inch wide all the way around. Spread 1/4 cup of the sauce over the lower half of the dough. Sprinkle 1/2 cup of the mozzarella over the sauce, and then top with one-quarter of the filling ingredient(s) and 1 Tbs. of the Parmigiano. Fold the top half of the dough over the filling. Crimp the dough either with fingers or a fork, sealing the damp edge tightly. Transfer the calzone to a baking sheet lined with parchment. Repeat with the remaining dough circles and filling ingredients. Brush the tops with olive oil, sprinkle lightly with kosher salt, if you like, and cut three steam vents in each.
Put the baking sheet in the oven (on the baking stone, if using) and reduce the oven temperature to 450°F. Bake until the crust turns a rich golden brown, 12 to 15 minutes. Remove from the oven and cool for 3 minutes before serving.
Substitute another soft melting cheese for the mozzarella, such as Monterey Jack, provolone, Gouda, smoked mozzarella, or smoked Gouda.
Substitute another dry aged grating cheese for the Parmigiano, such as Asiago or Romano.
Photo: Scott Phillips