Snip off & discard the ends of the green beans & cut them into 1/2" lengths. Drop the beans into 2 c of lightly salted boiling water, reduce the heat to moderate & cook briskly, uncovered, for 8 to 10 minutes, or until the beans are tender but still slightly resistant to the bite. Drain & run them under cold water.
In the same pan, combine the dashi, sugar, 1/4 ts salt, a sprinkle of soy sauce, sake. Bring to a boil over moderate heat, add the string beans & return to the boil. Remove the pan from the heat & cool to room temperature.
DRESSING: Over high heat, heat 3 tb sake to lukewarm. Removepan from heat & ignite the sake with a kitchen match, shaking the pan gently until the flame dies out. Pour the sake into a small bowl & cool to room temperature.
Add the sake, 2 ts sugar and 2 tbs soy sauce to the previously prepared sesame paste & mix together thoroughly.
Pour the sesame dressing into a large bowl, add the drained string beans & toss together until the vegetables are thoroughly coated. Taste for seasoning adding more salt if necessary. Serve at room temperature in small bowls, as a first course, salad or part of a Japanese meal.