Heat 2 tablespoons of oil in a large skillet over medium heat. Add the sausage and cook, stirring occasionally, until browned, about 6 minutes. (Don't fully cook the sausage, as it will be finished in the oven.) Drain the fat from the skillet.
Meanwhile, heat the remaining 2 tablespoons oil in a large skillet over medium-high heat. Add the onion and peppers and cook, stirring, until tender, about 2 minutes. Add in the remaining ingredients except for the mushrooms, cherry peppers, and Parmesan and cook, stirring occasionally, for another 3 minutes.
Combine the sausage, vegetable mixture, mushrooms, and cherry peppers in the gratin dish. Bake uncovered until well browned, about 40 minutes. Serve garnished with basil leaves and Parmesan.