1. Drain artichokes, reserving liquid. Chop artichokes and combine with roasted red pepper and basil in small bowl; cover and refrigerate.
2. Combine reserved artichoke liquid and Dijon mustard in small bowl. Place beef steaks and mustard mixture in food-safe plastic bag; turn steaks to coat. Close bag securely and marinate in refrigerator 6 hours or as long as overnight.
3. Remove steaks from marinade; 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.)
4. Carve steaks into thin slices. Season with salt and pepper, as desired. Serve with artichoke mixture.