For dressing, in small bowl whisk together vinegar, 2 tablespoons basil, garlic, 1 tsp. salt, and 1/2 tsp. black pepper. Slowly whisk in oil until smooth. Remove 2 tablespoons to marinate steaks; set remaining dressing aside.
Brush steaks with the 2 tablespoons dressing; let stand at room temperature for 30 minutes.
For charcoal grill, arrange medium-hot coals on one side of grill. Place steaks on rack directly over coals. Cover and lightly sear on both sides, 8 minutes. Move to unheated side of grill. Cover and grill 4 to 6 minutes more for medium rare (145 degrees F). Remove; let stand 5 minutes. (For gas grill, preheat to medium-high. Adjust for indirect grilling. Grill as above.)
Diagonally slice steaks; arrange on lettuce leaves with tomatoes and basil. Drizzle dressing; season with salt. Serves 4 to 6.