Whisk together first 7 ingredients in a small bowl. Set dressing aside.
Bring 4 cups water to a boil in a large saucepan. Add barley and salt; cover, reduce heat, and simmer 45 minutes. Remove from heat; let stand 5 minutes. Drain, if necessary. Stir in 1/3 cup dressing, reserving remainder.
Cook beans in boiling water until crisp-tender; drain. Plunge into ice water to stop the cooking process; drain and set aside.
Press cracked pepper over tuna. Grill, covered with grill lid, over high heat (400° to 500°) 3 minutes on each side or until desired degree of doneness.
Arrange tuna, barley, green beans, egg slices, and next 4 ingredients onto lettuce-lined plates. Drizzle with reserved dressing.