Brown the Sausage: Heat 1 tablespoon of 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).
Sauté the Vegetables: Add the sliced 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).
Finish the Filling: Add 1/2 cup marinara sauce and a splash of water to the skillet. Cook and stir until the vegetables are lightly coated and the skillet is mostly dry (3 to 5 minutes). Transfer the mixture to a medium bowl and wipe out the skillet.
Assemble the Quesadillas: Lay the tortillas on a work surface. On one side of each tortilla, layer 1/4 cup mozzarella, 1/2 tablespoon parmesan, a quarter of the sausage mixture, and another 1/4 cup mozzarella and 1/2 tablespoon parmesan. Fold the tortillas over the filling and press gently.
Grill and Serve: Brush the outside of the tortillas with the remaining tablespoon of olive oil. Working in two batches, cook the quesadillas in the reserved skillet over medium heat until browned, about 2 minutes per side. Slice into wedges and serve with the remaining warm marinara sauce for dipping.