Preheat a grill pan or saute pan over medium high heat. Add 2 tablespoons of the oil and heat until shimmering, almost smoking. Cook the sausages, turning with tongs or a wooden spoon, until nicely browned on all sides, 10 to 12 minutes total cooking time. Transfer to a cutting board and let cool. When cool enough to handle, coarsely chop the sausage.

Heat a wide, heavy saute pan over medium heat. Add remaining 2 tablespoons of oil and hear until its shimmering, almost smoking. Add the onion and pepper and cook, stirring with a wooden spoon, until tender, 8 to 10 minutes. Set aside and let cool in the pan.

Position a rack in the bottom of the oven and position a pizza stone in the center of the rack. Preheat the oven to 475F.

Dust your work surface and pizza peel with cornmeal.

Working with one ball of dough at a time, pat and stretch, or roll, the dough into an 8-inch circle on your work surface, then lift onto the peel in one swift movement. Working quickly, arrange one-sixth of the sausage, onion, pepper, fresh and smoked mozzarella, Parmesan, and ricotta in the center of the calzone. Gently fold the top of the dough over, stretching as needed to meet the edges of the other half. Pinch the edges to seal with your fingers, or with the tines of a fork. Use a sharp, thin-bladed knife to slash 2 small vents in the top.

Carefully transfer the calzone to the pizza stone. Bake until nicely golden brown cheese is bubbling through the vents, 8 to 10 minutes.

As the calzone bakes, make the next one and add it to the pizza stone. Work as quickly as you can and remove calzones as they are finished by sliding them onto the pizza peel and transferring them to individual serving dishes. Scatter more Parmesan over the top of the baked calzones, if desired, let rest for 5 minutes, then serve hot. If you work quickly and efficiently, the last calzone should be finished just a few minutes after the first one and you will be able to serve them all at once because they retain a lot of heat.