Preheat barbecue grill to medium-high. (Alternatively, warmth forged iron grill pan over medium-high warmth and brush with oil.) Lower romaine hearts in half, lengthwise. Brush lower sides with olive oil. Place romaine hearts, lower facet down, on grill and cook dinner, turning as soon as, till charred and barely wilted, about 3 minutes, relying on warmth. Switch, lower facet up, to serving platter. Scatter roasted vegetable salad overtop, dividing evenly amongst romaine hearts. Sprinkle with grated pecorino and drizzle with extra-virgin olive oil, balsamic vinegar, and chopped contemporary basil.