Heat olive oil in a large heavy enamel-lined casserole. Add peppers and onions and saute for a minute to get them cooking. Reduce heat to low, cover and simmer very gently until vegetables are tender, about 10 minutes. Don't let olive oil get too hot or you will change the flavor. While these are cooking, cut eggplant into 3/4inch chunks. When peppers and onions are tender, add the garlic, eggplant, tomatoes and thyme and simmer over low heat for 30 minutes.
While this is cooking cut zucchini and yellow squash lengthwise into halves or quarters, depending on how thick they are. Remove seeds with a spoon, then cut into 3/4 inch lengths. After 30 minutes of stewing eggplant, add zucchini and squash to stew, cover and simmer, over very low heat until all the vegetables are tender, about 20 minutes ( you can simmer for another 30 to 40 minutes for more meltingly tender vegetables). Strain the stew through a sieve and return juices back to casserole. Reduce the juices over medium heat until they begin to sizzle in the olive oil. Return this to the stew, season well to taste with salt and pepper. Divide ratatouille into two portions to proceed.