Preparation Bring broth to a simmer in a 3-quart saucepan, then add chicken and simmer, uncovered, 6 minutes. Remove pan from heat and cover, then let stand until chicken is cooked through, about 15 minutes. Transfer chicken to a plate and cool at least 10 minutes, reserving broth for another use. While chicken is poaching, bring 4 quarts salted cold water to a boil in a 5- to 6-quart saucepan over moderately high heat. Stir in noodles, then 1/2 cup cold water. When water returns to a boil, add another 1/2 cup cold water and bring to a boil again, stirring, then repeat once more, or until noodles are just tender but still firm and chewy throughout. Drain noodles in a colander and rinse well under cold water to cool, then drain well. Toss noodles with peanut oil in a large bowl. Stir together vinegar, soy sauces, chile oil with sediment, garlic, sugar, and salt in another bowl until sugar is dissolved, then add to noodles and toss until coated. Shred chicken with your fingers into 1/4-inch-wide strips and add to noodles, tossing to combine. Sprinkle with scallions and soy nuts.
Preparation Bring broth to a simmer in a 3-quart saucepan, then add chicken and simmer, uncovered, 6 minutes. Remove pan from heat and cover, then let stand until chicken is cooked through, about 15 minutes. Transfer chicken to a plate and cool at least 10 minutes, reserving broth for another use. While chicken is poaching, bring 4 quarts salted cold water to a boil in a 5- to 6-quart saucepan over moderately high heat. Stir in noodles, then 1/2 cup cold water. When water returns to a boil, add another 1/2 cup cold water and bring to a boil again, stirring, then repeat once more, or until noodles are just tender but still firm and chewy throughout. Drain noodles in a colander and rinse well under cold water to cool, then drain well. Toss noodles with peanut oil in a large bowl. Stir together vinegar, soy sauces, chile oil with sediment, garlic, sugar, and salt in another bowl until sugar is dissolved, then add to noodles and toss until coated. Shred chicken with your fingers into 1/4-inch-wide strips and add to noodles, tossing to combine. Sprinkle with scallions and soy nuts.