Heat the oil in a skillet over medium-high heat. Add the sausage and cook until it begins to brown, 3 to 4 minutes. Add the pepper and onion and continue to cook until the vegetables soften, about 3 minutes more, stirring frequently. With a slotted spoon, transfer the mixture to a bowl. Let cool slightly, then stir in the mozzarella.
Prepare the grill for indirect cooking over high heat (450° to 500°F). Preheat the stone over indirect high heat for 10 minutes
Divide the dough into 4 equal balls. On a lightly floured surface roll each ball into a circle, about 6 inches in diameter. Spoon some of the filling over half of each dough, leaving a 1/2-inch border. Fold the dough over the filling and tightly crimp the edges with your fingers or a fork. With the point of a sharp knife, cut 3 air vents in the top of each calzone. Lightly brush each calzone with the egg wash and season with salt.
Slide the calzones onto the stone. Cook over indirect high heat, with the lid closed, until the crust is golden brown, about 12 minutes. Remove from the grill and rest indoors for 5 minutes. Serve warm with marinara sauce for dipping.