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Heat 3 tablespoons of oil in a large nonstick pan over medium heat. Add the eggplant and season with ¼ teaspoon salt. Cook, stirring frequently, until soft and starting to brown, 10 to 12 minutes. Transfer to a plate and set aside.
Add another tablespoon of oil to the pan (no need to clean it). Add the zucchini and cook, stirring frequently, until tender-crisp, 3 to 4 minutes. Season with ¼ teaspoon salt and transfer to a plate; set aside.
Add two more tablespoons of oil to the pan and add the onion and bell pepper. Cook, stirring frequently, for about 5 minutes. Add the garlic and continue cooking for about 3 minutes more. Do not brown. Add the tomatoes and their juices, tomato paste, thyme, sugar, crushed red pepper flakes (if using) and ¾ teaspoon salt. Cook, stirring occasionally, until the tomatoes are broken down into a sauce, 8 to 10 minutes. Add the cooked eggplant to the pan; bring to a gentle boil, then reduce the heat to low, and simmer, uncovered, for about 10 minutes or until the eggplant is soft. Add the zucchini and cook for 1 to 2 minutes more, or until just warmed through. Taste and adjust seasoning, if necessary. Sprinkle with fresh basil and thyme, drizzle with a little olive oil if desired, and serve warm or chilled. Leftovers can be stored in the refrigerator in an airtight container for up to 5 days.