Heat 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Add the sausage and cook, breaking it up with a wooden spoon and stirring occasionally, until browned and mostly cooked through, about 5 minutes.
Add the bell peppers, onion, garlic, oregano, 1/2 teaspoon salt and a few grinds of pepper to the skillet. Cook, stirring occasionally, until the vegetables are tender, about 15 minutes. Add 1/3 cup each marinara sauce and water and cook, stirring, until the vegetables are lightly coated and the skillet is mostly dry, 3 to 5 minutes. Transfer to a medium bowl and carefully wipe out the skillet.
Lay the tortillas on a work surface. Top one side of each tortilla with 1/4 cup mozzarella, 1/2 tablespoon Parmesan, one-quarter of the sausage-and-peppers mixture and another 1/4 cup mozzarella and 1/2 tablespoon Parmesan. Fold the tortillas over the filling and gently press.
Brush the tortillas with the remaining 1 tablespoon olive oil. Working in two batches, cook the quesadillas in the reserved skillet over medium heat until browned, about 2 minutes per side.
Warm the remaining 1 cup marinara sauce in a small saucepan or the microwave. Cut the quesadillas into wedges. Serve with the sauce for dipping.