Step 1Place the eggplant chunks in a large colander and sprinkle liberally with salt. Toss to combine well and then set the colander aside on a plate or in the sink to drain while you prepare the remainder of the dish.
Step 2In a large skillet, heat 1/4 cup of olive oil over medium-high heat. Add the sliced onions and cook until they're slightly wilted, about 3 minutes. Add the bell peppers, thyme and oregano. Reduce the heat to medium, cover tightly and cook, shaking and stirring from time to time, until the peppers and onions are well softened, about 10 more minutes. Add the garlic and season to taste with salt. Stir well and, using a slotted spoon, transfer the cooked vegetables to a large pot, leaving as much oil as possible in the skillet.
Step 3Return the skillet to medium-high heat and add enough oil to film the bottom of the pan. Add the zucchini, season to taste with salt and cook, stirring, until it softens enough that you can cut a dent in it with the spatula. This will take anywhere from 5 to 10 minutes, depending on the age, size and quality of the squash. Using a slotted spoon, transfer the cooked squash to the onion pot, leaving as much oil as possible in the skillet.
Step 4Press the eggplant in the colander to remove as much moisture as possible, rinse it under running water, then turn it out onto a clean kitchen towel and pat it dry. Return the skillet to medium-high heat and, if necessary, add just enough oil to coat the bottom of the pan. When the oil sizzles, add the eggplant. Cook, stirring, until the eggplant softens enough that you can cut a dent in it with a spatula. Again, this will vary from 5 to 10 minutes depending on the age, size and quality of the eggplant.
Step 5When the eggplant has softened, add the tomatoes, vinegar and a generous grinding of pepper and cook until the tomatoes have melted and the vinegar has lost its raw smell, 3 to 5 minutes.
Step 6Combine all of this, including whatever oil remains, with the other cooked vegetables in the pot. Stir well and taste: There should be several layers of sweetness but also an underlying tartness that is noticeable. If necessary, add up to another tablespoon of vinegar. The dish can be prepared to this point and refrigerated, tightly covered, until ready to serve.
Step 7When ready to serve, heat the ratatouille, taste again to correct the seasoning and add the torn basil leaves at the last minute to keep them from discoloring. Turn the dish into a warmed serving bowl and pass at the table.