Place eggplant in colander. Sprinkle with salt; let stand 30 minutes.
Pat dry with paper towels.
Heat 1/4 cup olive oil in large, heavy nonstick skillet over medium-high heat.
Add eggplant and saute until brown and cooked through, about 6 minutes.
Transfer eggplant to large bowl.
Heat 1 tbsp oil in same skillet over medium-high heat. Add peppers and saute until light brown, about 5 minutes.
Add peppers to eggplant.
Add 1 tbsp oil to skillet; saute onion for about 4 minutes.
Add onion to eggplant.
Heat 1 tbsp oil in skillet; add zucchini and brown lightly, about 3 minutes.
Add to other vegetables.
Heat 1 tbsp oil in skillet; add tomatoes, garlic, thyme, and bay leaf.
Saute 3 minutes.
Return all vegetables to skillet.
Reduce heat to medium; cover and cook until vegetables are very tender, stirring occasionally, about 20 minutes.
Season to taste with salt and pepper.
Mix in vinegar; discard bay leaf. Mix in basil and serve.