1 1/2 pounds large tomatoes, such as beefsteak, cut in half crosswise
1 medium sweet onion, such as Vidalia, peeled and cut in half crosswise
3 large cloves garlic, unpeeled
1 tablespoon plus 1 teaspoon extra-virgin olive oil, divided
1/4 teaspoon salt, or to taste
Freshly ground pepper, to taste
2 cups reduced-sodium chicken broth, or vegetable broth, divided
1/4 cup tomato juice
1 teaspoon tomato paste
1/4 teaspoon Worcestershire sauce
1 tablespoon fresh basil, chopped
Brown sugar, to taste (optional)
1/2 cup corn kernels, (fresh, from 1 ear, see Tip) or frozen, thawed