In a medium saucepan cook green beans, covered, in a small amount of boiling salted water about 10 minutes or until crisp-tender, adding carrots the last 5 minutes of cooking. Drain; set vegetables aside.
In the same saucepan melt butter; stir in cornstarch. Add the teriyaki sauce and water. Cook and stir until thickened and bubbly. Return vegetables to saucepan; toss gently to coat. Heat through. If desired, sprinkle each serving with sesame seeds. Makes 6 to 8 servings.