1. Soak skewers in water at least 30 minutes.
2. Combine 1 tablespoon each soy sauce, mirin, and sake in a medium bowl. Add beef, tossing to coat. Let stand 30 to 90 minutes.
3. Combine remaining 3 tablespoons each soy sauce and mirin, remaining 1 tablespoon sake, and sugar in a small saucepan over medium-high heat. Simmer 5 to 8 minutes or until glaze is slightly syrupy. Set aside.
4. Combine green onions and sesame oil; toss well. Thread green onion pieces and beef alternately onto skewers. Cover and chill until ready to grill.
5. Grill skewers over medium-high heat (350° to 400°) 1 minute. Turn skewers over; brush with glaze, and grill 1 to 2 minutes or until desired degree of doneness.
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