Place beef steak and 1/2 cup pesto in food-safe plastic bag; turn to coat steak. Close bag securely; marinate in refrigerator 6 to 24 hours, turning occasionally.
Remove steak from marinade; discard marinade. Place steak on grid over medium, ash-covered coals. Grill, covered, 7 to 12 minutes (over medium heat on preheated gas grill 8 to 12 minutes) for medium rare (145°F) to medium (160°F) doneness, turning occasionally. Carve steak diagonally across the grain into thin slices.
Combine remaining pesto with mayonnaise in small bowl.
Spread cut sides of hoagie rolls with pesto-mayo mixture. Layer bottom of rolls with equal amounts beef; top with artichoke hearts and cheese slice.
Place open-faced sandwiches on rack of broiler pan, with hoagie roll tops, cut-side-up next to sandwiches, so surface of sandwich is 2 to 3 inches from heat. Broil 1 minute or until cheese is melted and cut sides of buns are toasted. Close sandwiches.
Nutrition information per serving: 572 Calories; 279 kcal Calories from fat; 31 g Total Fat; 11 g Saturated Fat; 5 g Monounsaturated Fat; 76 mg Cholesterol; 893 mg Sodium; 41 g Total Carbohydrate; 4.7 g Dietary Fiber; 31 g Protein; 3.3 mg Iron; 4.7 mg NE Niacin; 0.3 mg Vitamin B6; 2.4 mcg Vitamin B12; 3.3 mg Zinc; 10.9 mcg Selenium; 59.6 mg Choline;