For the peppers: Place an oven rack in the center of the oven and preheat to 400 degrees F. Spray a small baking dish or baking sheet with vegetable oil cooking spray. Arrange the peppers, cut side-up, on the baking sheet and drizzle with the olive oil. Bake until the peppers are tender but still holding their shape, about 20 minutes.
For the eggplant: Heat the vegetable oil over medium-high heat in a 12-inch nonstick skillet. Add the eggplant in batches and cook, stirring frequently, until golden, 15 to 20 minutes. Drain on paper towels and season with salt.
For the filling: Combine the cooked eggplant, tomato-basil sauce, olives, capers, salt and pepper in a 12-inch nonstick skillet. Bring to a simmer and cook until slightly thickened, about 8 minutes.
For the topping: In a small bowl, combine the breadcrumbs and Parmesan.
Preheat the broiler.
Spoon the filling into the bell peppers and sprinkle the topping over the filling. Drizzle with the olive oil and broil until a golden crust forms, 2 to 3 minutes.