Heat grill to medium high or high heat.
Cut romaine lettuce lengthwise, leaving the cores attached to hold the lettuce together.
Use a brush to lightly coat the cut side of the lettuce, and then salt and pepper to taste.
Cut the onion into large chunks. I left the onion attached to the core so I could grill it in chunks, but it would be easier if put on a BBQ skewer.
Brush the onion and mini peppers with olive oil, and lightly salt and pepper.
Add the peppers and onions to the grill, and grill for about 5 minutes. Turn over, and place to the sides of the BBQ.
Place the romaine cut-side down on the grill, and grill for about 3 minutes, until lightly charred.
Remove romaine from grill, and then remove the onions and peppers once they're cooked to taste.
Drizzle the romaine with lemon juice, and top with sliced cherry tomatoes, olives, basil, the grilled peppers and onions, and parmesan cheese.
Serve with a good knife for cutting.