Preheat oven to 375°F / 190°C. Toss eggplant with 2 tablespoons olive oil, a pinch of salt and pepper.
Place eggplant on sheet pan and roast in oven for 20 minutes.
Toss zucchini and summer squash with 2 tablespoons olive oil and a pinch of salt and pepper.
Place zucchini and summer squash on sheet pan and roast for 15 minutes.
While eggplant, zucchini and summer squash are roasting, heat 2 tablespoons of olive oil in a large, heavy-bottomed pot over medium heat.
Add onions and peppers to pot and sauté for 10 minutes until softened, but not browned.
Add garlic, thyme & bay leaves, season with salt and pepper.
Add tomatoes and cook over medium-low heat for 10 - 15 minutes until tomatoes have released their juices, then raise heat and simmer for several minutes to allow some of the liquid to evaporate, if desired. (*see note)
Remove eggplant, zucchini and summer squash from the oven and add to the pot. Stir to combine. Taste and adjust seasoning.
Let simmer for a few minutes allowing flavors to combine, remove from heat and stir in parsley and basil.