While assembling the other ingredients, soak the noodles in hot water to soften, 10 to 15 minutes. Drain and set aside.
To make the sauce, in a bowl, whisk together the chicken broth with the cornstarch. Add the soy, hoisin, sugar, and sherry, if using, whisk, and set aside.
Heat a wok over high heat. Add the oil and when hot and nearly smoking, add the green onions, garlic, ginger, and red pepper flakes and cook, stirring, for 10 to 15 seconds. Add the chicken and stir-fry until turning opaque and nearly cooked through, 3 to 4 minutes. Add the vegetables and stir-fry for 1 minute. Add the sauce, stir and toss, cooking until the chicken is all the way cooked through and the sauce is thick, about 2 minutes. Remove the chicken and vegetables from the pan. Add the noodles, toss, and cook to warm through, 30 seconds to 1 minute.
Transfer the stir-fry to a platter and garnish with additional green onions. Arrange the noodles on the side and serve immediately.