In a large bowl, combine the first six ingredients. Add tomatoes and onions; toss to coat. Transfer to a grill wok or basket.* Grill, covered, over medium heat for 8–12 minutes or until tender, stirring frequently. Set aside.
For the grilled romaine, cut the romaine hearts in half lengthwise, leaving ends intact. Brush with oil. Sprinkle with salt and pepper. Place the romaine halves cut sides down, directly on the grill. Grill, covered, over medium heat for 3–4 minutes on each side or until leaves are slightly charred and wilted.
For the dressing, place the oil, vinegar, garlic and brown sugar in a food processor; cover and process until smooth.
Coarsely chop the romaine; divide among 10 salad plates.
Top with tomato mixture; drizzle with dressing. Sprinkle with cheese if desired.
*If you do not have a grill basket, use a disposable foil pan. Poke holes in the bottom with a meat fork to allow any liquid to drain.
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