Preheat the oven to 500°F.
In a heavy pan over medium heat, warm the oil. Add the onion and garlic, lower the heat, and cook for 10 minutes, or until the onion begins to wilt. Add the eggplant, stir, and cook for 5 minutes. Add the zucchini, bell pepper, and tomatoes, toss, and cook for 5 minutes. Add the basil, salt and pepper, and vinegar and stir to blend.
Cover, raise the heat to medium, and cook for 30 minutes. If there is too much liquid, uncover and cook until the juice has been reduced.
Pour the mixture into the piecrust and finish with a lattice top.
Bake for 10 minutes, then reduce the heat to 350°F and cook for 15 minutes, or until golden.