Preheat the oven to 375°F.

In a 3.5-quart braiser or large baking dish, combine the eggplant, cherry tomatoes, onion, zucchini, bell pepper, and garlic. Add 3 tablespoons olive oil, balsamic vinegar, tomato paste, 1½ teaspoons salt, 1 teaspoon pepper, crushed red pepper flakes, oregano, and thyme. Toss until the vegetables are evenly coated, then spread them into a single, even layer.

Nestle the chicken thighs into the vegetables, skin side up. Pat the chicken dry with a paper towel, then drizzle with the remaining 1 tablespoon olive oil, rubbing to evenly coat the skin. Sprinkle the tops of the chicken with the remaining 1 teaspoon salt and 1 teaspoon pepper.

Roast, uncovered, for 45 to 50 minutes, or until the chicken skin is golden and crisp and the vegetables are tender and jammy, almost stew-like.

Remove from the oven and let rest for a few minutes before serving. Garnish with fresh torn basil leaves.