How to Make It
In a pot of boiling, salted water, cook the vermicelli until just done, about 9 minutes. Drain. Rinse with cold water; drain thoroughly.
In a medium saucepan, combine the 1 cup broth, one third of the scallions, and the salt. Bring to a simmer, add the chicken, stir, and cover the pan. Simmer for 5 minutes. Turn the heat off and let the chicken steam for 5 minutes. Remove the chicken from the saucepan and shred it.
In a blender, puree the remaining 3 tablespoons broth, the ginger, garlic, tahini, sesame oil, sugar, cooking oil, red-pepper flakes, soy sauce, and pepper. Put the cucumber halves cut-side down and slice them lengthwise into thin strips.
To serve, put the vermicelli on plates or in bowls. Scatter each serving with a layer of cucumber strips and then top with the shredded chicken. Pour the sesame sauce over the chicken and sprinkle with the remaining scallions.