Whisk marinade ingredients in medium bowl. Place beef steaks and 1/2 cup marinade in food-safe plastic bag; turn steaks to coat. Close bag securely and marinate in refrigerator 15 minutes to 2 hours. Cover and refrigerate remaining marinade for dressing.
Preheat charcoal grill to medium heat.
Remove steaks from marinade; discard marinade. Sprinkle steaks with pepper. Place steaks in center of grill over medium, ash-covered coals; arrange onion around steaks.
Grill steaks, uncovered, 15 to 18 minutes for medium-rare to medium doneness, turning occasionally. Grill onions 15 to 20 minutes or until tender, turning occasionally.
Carve steaks into slices. Cut onion slices into quarters. Toss cabbage, onion and 2 tablespoons reserved dressing in large bowl. Arrange beef on cabbage mixture. Drizzle with some of the dressing. Pass remaining dressing.
To prepare on gas grill, preheat grill according to manufacturer's directions for medium heat. Grill steaks, covered, 11 to 15 minutes for medium rare to medium doneness, turning occasionally. 2 beef shoulder petite tender roasts (8 to 12 ounces each) or 2 beef shoulder center steaks (ranch), cut 1-inch thick (about 8 ounces each) may be substituted for top loin (strip) steaks. Grill shoulder petite tender roasts, covered, over medium, ash-covered coals l4 to 18 minutes (over medium heat on preheated gas grill, covered, 14 to 19 minutes) for medium-rare to medium doneness, turning occasionally. Grill shoulder center steaks, covered, over medium, ash-covered coals 11 to 14 minutes (over medium heat on preheated gas grill, covered, 12 to 16 minutes) for medium-rare to medium doneness, turning occasionally.
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Recipe courtesy American National CattleWomen, Inc. created by Kurt Wait, Redwood City, CA