Cut an X in bottom of each tomato with a sharp paring knife and blanch together in a 4-quart pot of boiling water 1 minute. Transfer tomatoes with a slotted spoon to a cutting board and, when cool enough to handle, peel off skin, beginning from scored end, with paring knife.
Coarsely chop tomatoes and transfer to a 5-quart heavy pot with garlic, parsley, basil, and 1/3 cup oil. Simmer, partially covered, stirring occasionally, until tomatoes break down and sauce is slightly thickened, at least 30 minutes.
While sauce is simmering, toss eggplant with 1/2 teaspoon salt in a large colander and let stand in sink to drain until ready to use.
Meanwhile, cook onions in 2-3 tablespoons oil in a 12-inch heavy skillet over moderate heat, stirring occasionally, until softened, 10 to 12 minutes. Transfer onions with a slotted spoon to a large bowl, then add 2-3 tablespoons oil to skillet and cook 1 cup okra over moderate heat, stirring occasionally, until softened, about 6-8 minutes. Transfer peppers with slotted spoon to bowl with onions. Add 2-3 tablespoons oil to skillet and cook zucchini with 1/4 teaspoon salt over moderate heat, stirring occasionally, until just tender, 6 to 8 minutes. While zucchini are cooking, pat eggplant dry with paper towels. When done, transfer zucchini with slotted spoon to bowl with other vegetables.
Add 2-3 tbsp. oil to skillet and cook eggplant over moderate heat, stirring occasionally, until softened, 10 to 12 minutes. Add to vegetable bowl.
To the tomato sauce, add vegetables, and simmer, covered, stirring occasionally, until vegetables are very tender, about 30 minutes and up to 1 hour. Season with salt and black pepper to taste. Cool uncovered, and serve warm or at room temperature.
·Stew can be made 2 days ahead and chilled, covered. Bring to room temperature or reheat before serving.