Cut beef steak into 1-1/4-inch pieces. Alternately thread beef and green onion pieces evenly onto four 10-inch metal skewers. Sprinkle with 1-1/2 teaspoons steak seasoning.
Thread onion wedges onto another four 10-inch metal skewers, alternating onion varieties. Brush onion wedges with oil; sprinkle with remaining 1-1/2 teaspoons steak seasoning.
Place onion wedge kabobs on grid over medium, ash-covered coals. Grill, covered, 15 to 20 minutes, turning occasionally. (Gas grilling times remain the same.) About 10 minutes before onions are done, move kabobs to outer edge of grid. Place beef kabobs in center of grid; grill, covered, 8 to 10 minutes (over medium heat on preheated gas grill, 9 to 11 minutes) for medium rare (145°F) to medium (160°F) doneness, turning once.
Sprinkle onion and beef kabobs with cheese before serving.
Nutrition information per serving: 279 Calories; 99 kcal Calories from fat; 11 g Total Fat; 4 g Saturated Fat; 5 g Monounsaturated Fat; 56 mg Cholesterol; 696 mg Sodium; 15 g Total Carbohydrate; 2.4 g Dietary Fiber; 29 g Protein; 2.1 mg Iron; 7.7 mg Niacin; 0.8 mg Vitamin B6; 1.6 mcg Vitamin B12; 5.3 mg Zinc; 32.5 mcg Selenium;