Drain artichokes, reserving liquid. Chop artichokes and combine with roasted red pepper and basil in small bowl; cover and refrigerate.
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.
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 gas grill, 17 to 19 minutes) for medium rare (145°F) doneness, turning occasionally. (Do not overcook.)
Carve steaks into thin slices. Season with salt and pepper, as desired. Serve with artichoke mixture.
Nutrition information per serving: 432 Calories; 126 kcal Calories from fat; 14 g Total Fat; 3 g Saturated Fat; 4 g Monounsaturated Fat; 119 mg Cholesterol; 984 mg Sodium; 19 g Total Carbohydrate; 3.1 g Dietary Fiber; 55 g Protein; 4.7 mg Iron; 9.8 mg NE Niacin; 0.7 mg Vitamin B6; 3 mcg Vitamin B12; 8.8 mg Zinc; 57.3 mcg Selenium;