Thoroughly wash 1 eggplant and 1 pound of zucchini under cool, running, drinkable water. Cut eggplant into 1-inch cubes; set aside. Cut zucchini into 1-inch half moons; set aside.
In a large bowl, toss the eggplant with 2 tablespoons of extra-virgin olive oil, ½ teaspoon of kosher salt, and a few cranks of freshly ground black pepper; toss until evenly coated. Transfer to a baking sheet and arrange the eggplant cut-side down.
In the same large bowl, repeat with zucchini. Add 2 tablespoons of extra-virgin olive oil, ½ teaspoon of kosher salt, and a few cranks of freshly ground black pepper to taste, tossing and transferring to a second baking sheet.
Roast until the vegetables are tender and the undersides are golden brown, about 40 minutes—the eggplant and zucchini may differ in cooking time, and that is fine; remove each when cooked to perfection. Let the vegetables rest for 5 minutes on the baking sheet before removing with a thin spatula. This gives them a chance to steam themselves off the pan’s surface, so you don’t leave any of their sweet crust behind!
Meanwhile, thoroughly wash 1 orange bell pepper, 1 yellow bell pepper, and 20 fresh basil leaves under cool, running, drinkable water. Cut bell peppers into 1-inch squares; set aside.
Chiffonade the basil by stacking several leaves on top of each other, with the largest on the bottom. Roll them up crosswise and thinly slice crosswise from one end of the roll to the other. Set aside.
Dice 1 onion and mince ½ teaspoon of fresh thyme.
In a large sauté pan over medium heat, add 2 tablespoons of extra-virgin olive oil. Add the cut bell peppers, diced onion, and minced thyme to the heated pan. Cook until the onions are translucent and the bell peppers have softened, about 5 minutes.
Mince 4 cloves of garlic, add to the pan and cook for 2 more minutes. Add one28-ounce can of diced tomatoes and ⅓ cup of pitted and quartered Kalamata olives. Cook, partially covered, until the tomatoes break down and the mixture is thickened slightly, about 10 minutes.
Stir in roasted eggplant and zucchini, and season to taste with kosher salt and freshly ground black pepper. Stir fresh basil in at the last minute, so it just wilts. Serve warm or at room temperature. Eat up, Mama!