Place the chicken in a bowl and toss with 1 tablespoon soy sauce. Let sit while you prep the remaining ingredients. In a small bowl or large liquid measuring cup, combine the three-quarters of the green onions, the remaining 3 tablespoons soy sauce, hoisin, garlic, ginger, and vinegar. Set near the stove. Reserve the remaining green onions for serving. Bring a large pot of salted water to a boil. Cook noodles until they are about 1 to 2 minutes from done, according to package instructions. They should be very al dente, still a little too firm to eat, but not excessively hard and chewy. Drain and toss with 1/2 tablespoon of the oil to prevent sticking. In a large skillet over medium-high heat, heat 1/2 tablespoon oil. Once the oil is hot, add the chicken. Cook until golden and fully cooked through, about 3 to 4 minutes. Remove to a plate. To the now-empty skillet, add the remaining 1 tablespoon oil. Add the vegetables and cook until they begin to brown and soften but are still fairly crisp, about 3 to 4 minutes. Add half the scallion mixture and saute until fragrant, about 1 minute. Add the noodles. Cook, using tongs to toss the noodles and coat them with the sauce, for 30 seconds. Add the eggs, sriracha, chicken, and remaining scallion mixture. Continue to stir fry and toss the noodles, until the eggs are cooked through and the noodles are tender, 1 to 2 minutes longer. Remove from heat. Sprinkle with the reserved green onions.