Preheat the oven to 500 degrees F and place a pizza stone in the bottom of the oven. (Alternatively, lightly oil 2 baking sheets. Set aside.)
Place the 4 portions of dough on a lightly floured surface. Divide the ham and salami evenly among 1 side of each of the dough circles. Top each calzone with 6 tablespoons of the ricotta cheese and divide the mozzarella cubes, grated Parmesan and basil evenly among the calzones over the ricotta. Sprinkle each calzone with 1/8 teaspoon of salt and 1/8 teaspoon of crushed red pepper. Fold the untopped half of dough over the filling, rolling the top edge underneath the bottom and pressing edges together with your fingertips to seal, crimping as you go along. Cut several small slits in the top of each calzone and transfer calzones to a pizza peel, in batches if necessary, using cornmeal to help facilitate moving the dough. Transfer the calzones to the preheated baking stone in the preheated oven and cook for 10 to 12 minutes, or until golden brown and dough is cooked through. Remove from the oven with a metal peel or spatula and serve immediately.
In a large bowl combine yeast with water and sugar and stir well to combine. Set aside until foamy, about 5 minutes. Add the salt, olive oil, and half of the flour and mix well to thoroughly combine. Add all remaining flour except 1/2 cup and mix well with your hands, working to incorporate the flour little by little. The dough should be slightly sticky to the touch. Transfer dough to a lightly floured work surface and knead dough for at least 5 and up to 7 minutes, adding enough additional flour, as necessary, to form a smooth and elastic dough that is not sticky. Transfer dough to a lightly oiled 2 or 3-quart bowl and turn to coat with oil. Cover with a damp towel and let rise in a warm place until doubled in size, usually at least 1 hour.
Preheat oven to 500 degrees F and if you have one, place a pizza stone on the bottom rack of the oven.
Divide dough into 2 portions (for 2 (12 to 14-inch) pizzas and form into balls. (See note below for calzones.) Place on a lightly oiled baking sheet and cover with a damp towel. Let rest for 15 minutes, then transfer to a lightly floured surface, shape as desired and roll out to a 1/8-inch thickness. Transfer dough to a pizza peel (sprinkle with cornmeal to help facilitate moving dough) and top with toppings of choice. Transfer to the preheated pizza stone and bake until crispy and golden brown, usually 12 to 18 minutes (depending on the toppings and the thickness of the crust). Remove from the oven with a metal peel or spatula and serve immediately.
For calzones, divide the dough into 4 equal portions and form into 4 balls. Place on a lightly oiled baking sheet and cover with a damp towel. Let rest for 15 minutes, then transfer to a lightly floured surface and roll out into 4 (10-inch) circles. Place filling of choice in the center of 1 side of each circle, then fold dough over filling to meet edges of filled side. Crimp edges with a fork or your fingers, then cut a small slit in the top of the calzone to allow steam to escape while cooking. Cook on a preheated pizza stone or backs of cookie sheets in a preheated 475 degree F oven for about 10 to 12 minutes, or until well-browned. Remove from the oven with a metal peel or spatula and serve immediately.