Toss tomatoes, onion, and garlic in a mixing bowl with 1 tablespoon oil. Season with salt and pepper. Spread on the prepared baking sheet and roast until the vegetables are soft and caramelized, about 30 minutes. Let cool.
Peel and seed the tomatoes. Trim off the onion ends. Peel the garlic. Place the vegetables in a food processor or blender with 1 cup broth and the remaining 1 teaspoon oil. Pulse to desired thickness and texture.
Transfer the vegetable puree to a large, heavy pot or Dutch oven. Add the remaining 1 cup broth, tomato juice, tomato paste, Worcestershire sauce, basil, and brown sugar (if using). Bring to a simmer over medium heat, stirring often. Ladle into six soup bowls; garnish with corn and serve.
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