Step 1Heat 1 tablespoon oil in 10- to 12-inch wide pot over medium heat. When very hot, add onions. Cook, covered, stirring occasionally, until onions are softened, about 10 minutes. Then, cook, uncovered, stirring often, until onions turn a light brown but are nowhere near burning, about 8 to 10 minutes more.
Step 2Add zucchini, garlic (reserve 1 teaspoon for finish) and 1 teaspoon salt. Stir well. Cook 5 minutes, shaking pan occasionally to mix. Add peppers, tomatoes, bay leaves, thyme and red pepper flakes. Cook, uncovered, shaking pan often to prevent sticking, until just tender, about 20 to 25 minutes.
Step 3Heat 1 tablespoon oil in 12-inch nonstick skillet over medium-high heat until very hot. Add 1/2 eggplant, sprinkled with 1/4 teaspoon salt. Brown quickly, shaking pan, about 2 minutes. Set aside. Repeat with 1 tablespoon oil and remaining eggplant.
Step 4Add eggplant to cooked vegetables. Bring to simmer; stir well. Add remaining oil, garlic, vinegar, tomato paste and herbs (start with 1 tablespoon vinegar and tomato paste). Stir well; cook 1 more minute. Remove from heat. Taste and adjust seasoning as needed with vinegar, tomato paste, salt, herbs. Can be served immediately. (Can also be refrigerated up to 1 week or frozen up to 1 month. To serve, bring to room temperature if chilled. Stir well; taste and adjust seasoning. Serve at room temperature, warm or hot.)