Place parsley and 4 cloves garlic in food processor or blender container. Cover; process until finely chopped. Add lime juice, oil and salt; process just until just blended. Refrigerate until ready to use.
Mince remaining clove garlic and rub over both sides of beef Steak. Place Steak in center of grid over medium, ash-covered coals; arrange bell pepper around Steak. Grill Steak, covered, 11 to 15 minutes (over medium heat on preheated gas grill, 13 to 16 minutes) for medium rare (145°F) to medium (160°F) doneness, turning occasionally. Grill bell pepper 6 to 8 minutes (gas grill times remain the same) or until tender, turning occasionally.
Carve Steak into thin slices. Cut pepper halves into strips. Season beef and peppers with salt and pepper. Spread cut sides of rolls with parsley mixture. Evenly layer beef, pepper strips and cheese over parsley mixture. Close sandwich. Place sandwiches back on grill; grill, covered, 2 to 3 minutes.
Nutrition information per serving: 539 Calories; 216 kcal Calories from fat; 24 g Total Fat; 9 g Saturated Fat; 9 g Monounsaturated Fat; 89 mg Cholesterol; 780 mg Sodium; 39 g Total Carbohydrate; 3.5 g Dietary Fiber; 41 g Protein; 4.9 mg Iron; 14.7 mg NE Niacin; 0.7 mg Vitamin B6; 1.9 mcg Vitamin B12; 6.1 mg Zinc; 35.1 mcg Selenium; 109.1 mg Choline;