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- Combine all marinade/sauce ingredients except mayonnaise in small bowl; mix well. Divide mixture in half. Place beef steaks and 1/2 of mixture in food-safe plastic bag; turn steaks to coat. Close bag securely and marinate in refrigerator 6 hours or as long as overnight. Stir mayonnaise into remaining 1/2 of mixture for sauce; cover and refrigerate.
- Remove steaks from marinade; discard marinade. Place steaks on grid over medium, ash-covered coals. Grill, covered, 13 to 15 minutes (over medium heat on preheated grill, 17 to 19 minutes) for medium rare (145°F) doneness, turning occasionally. (Do not overcook.) Season steaks with salt, as desired. Serve with sauce.