Drain artichokes; reserve liquid. Chop artichokes; combine with red pepper and basil. Refrigerate.
Mix reserved artichoke liquid and mustard. Marinate beef steaks in mustard mixture in refrigerator 6 hours or as long as overnight.
Remove steaks; discard marinade. Place steaks on grid over medium, ash-covered coals. Grill, uncovered, 19 to 23 minutes for medium rare doneness, turning occasionally. (Do not overcook.) Carve steaks. Serve with artichoke mixture.