Trim fat from steaks. Season steaks with salt and pepper. For a charcoal grill, place steaks on the rack of an uncovered grill directly over medium coals. Grill until desired doneness, turning once. Allow 11 to 15 minutes for medium rare (145 degree F) or 14 to 18 minutes for medium doneness (160 degree F).
Meanwhile, for relish, grill onion, mushrooms, and tomatoes directly over medium coals until tender, turning once halfway through grilling. Allow 15 minutes for onion and 10 minutes for mushrooms and tomatoes. (For a gas grill, preheat grill. Reduce heat to medium. Place steaks, then vegetables on grill rack over heat. Cover and grill as above.)
Cut onion, mushrooms, and tomato halves into 1-inch pieces. In a medium bowl stir together basil, garlic, olive oil, the 1 teaspoon kosher salt, and the 1 teaspoon cracked black pepper; stir in grilled vegetables. To serve, spoon warm relish over steaks. Makes 4 sesrvings.