Combine Rub ingredients; press evenly onto beef steaks.
Place steaks on grid over medium, ash-covered coals. Grill, covered, 11 to 14 minutes (over medium heat on preheated gas grill 11 to 15 minutes) for medium rare (145°F) to medium (160°F) doneness, turning occasionally.
Carve steaks into slices. Place lettuce leaves on serving platter. Evenly layer vegetables onto lettuce leaves. Top evenly with steak. Drizzle with vinaigrette; sprinkle with cheese and nuts, if desired.
Nutrition information per serving: 90 Calories; 40.5 kcal Calories from fat; 4.5 g Total Fat; 1.5 g Saturated Fat; 0 g Trans Fat; 0.4 g Polyunsaturated Fat; 1.7 g Monounsaturated Fat; 25 mg Cholesterol; 90 mg Sodium; 3 g Total Carbohydrate; 1 g Dietary Fiber; 9 g Protein; 1 mg Iron; 175.4 mg Potassium; 3.6 mg NE Niacin; 0.2 mg Vitamin B6; 0.5 mcg Vitamin B12; 1.6 mg Zinc; 9.6 mcg Selenium; 33 mg Choline;