Heat a grill pan or indoor/outdoor grill to high. Drizzle extra-virgin olive oil over the tuna steaks spread it around then season with salt and pepper.
Combine tomatoes, onions, parsley and basil in a bowl. Dress with extra-virgin olive oil, enough to coat the tomatoes evenly, 2 to 3 tablespoons. Season the tomatoes with salt and pepper, to taste. Let the sauce marinate at least 10 minutes.
When you are ready to eat, grill steaks 2 minutes on each side for rare, 3 minutes for medium and 4 for opaque, well done. Stir sauce up then serve liberal amounts of it on top of the steaks.