Combine the ½ cup San-J Asian BBQ Sauce, 2 tablespoons olive oil and 1 tablespoon balsamic vinegar in a large plastic storage bag. Add the steak, close the bag and toss to coat the steak. Let marinate at room temperature for 20 minutes or in the refrigerator for up to 12 hours. (If marinating in the refrigerator, let sit at room temperature for 20 minutes before grilling.)
Preheat grill to medium heat (350 – 400 degrees). Brush the grates of the grill with oil. Remove the steak from the marinade and dry with paper towels. Discard the marinade. Grill the steak with the lid of the barbeque closed for 8 – 10 minutes for medium rare, turning once. Remove the steak from the grill, place on a platter and cover with foil. Let rest for 15 minutes.
While the steak is resting, prepare the salad. Cut the romaine hearts and radicchio into quarters, lengthwise. Slice the onion into ½ inch thick slices. Brush with some olive oil and sprinkle with a little salt and pepper. Place the onions on the grill and cook with the lid closed for 5 minutes. Turn the onion slices over, add the lettuce and radicchio and cook for about 5 minutes (along with the onions) turning 3 or 4 times or until slightly wilted with some brown spots. Remove from grill and cut the lettuce into large chunks. Separate the onion rings. Whisk together the 3 tablespoons olive oil, 1 tablespoon balsamic vinegar and 1 tablespoon San-J Asian BBQ Sauce together in a large mixing bowl. Add the lettuce, radicchio and onions and toss to coat. Place on a platter. Slice the steak thinly and place on top of the salad. Scatter tomatoes around.