Preheat a grill pan or sauté 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 sauté pan over medium heat. Add remaining 2 tablespoons of oil and hear until it’s 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 475°F.