Rinse and dry the peppers. Remove and discard core and seeds and cut lengthwise into 1/2-inch strips. Rinse, scrub and drain zucchini and eggplant. Cut away any blemishes.
Cut the zucchini crosswise into about 1/4 -inch thick slices, and the eggplant lengthwise into 2- or 3-inch strips, about 1/2-inch wide. Dab the cut vegetables with several layers of paper toweling to sop up moisture.
Heat 2 tablespoons oil in a large heavy skillet or Dutch oven over medium-high heat. Add the zucchini and eggplant and sauté, turning frequently and adding a little more oil if needed, for 5 to 7 minutes or until the vegetables are opaque in color and softened. Remove the cooked vegetables from the pan, place in a bowl, and sprinkle with salt.
If needed, add a little more oil to the pan. Reduce heat to medium low. Add bell peppers, garlic, onion, basil (or cilantro or parsley), and sauté, stirring, for about 7 minutes or until the peppers are tender.
Push the vegetables to one side of the pan, add the tomatoes and cook for 3 or 4 minutes, or until the tomatoes soften. Return the eggplant and zucchini to the pan, sprinkle in the remaining salt and black pepper, mixing well but gently.