Prepare Fresh Tomato Salsa. Place beef rib eye steaks in utility dish; sprinkle both sides of steaks with lime juice, rubbing into surface. Cover and refrigerate while preparing coals. Wrap tortillas securely in heavy-duty aluminum foil. Place steaks on grid over medium coals (see notes). Grill steaks 7 to 9 minutes for rare to medium, turning once. Place tortilla packet on outer edge of grid, five minutes before end of cooking time. Heat tortillas 5 minutes, turning once. Top each steak with equal amounts of each cheese 1 minute before end of cooking time. Trim excess fat from steaks; carve steaks into slices.
Combine tomato, green onion, cilantro, wine vinegar, jalape?o pepper, garlic, salt and black pepper; cover and reserve until ready to use.
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