Put the chicken to a small bowl with the egg white, garlic, if using, 1 tablespoon of the soy sauce and some pepper. Combine and let marinate for at least 30 minutes and up to an hour in the refrigerator.
Place the dry rice noodles in a bowl and cover with hot water. Let the noodles soak until they are white and soft but not mushy, about 10 minutes. Drain and set them aside. (if you use a sheet of fresh rice noodles, cut them into 1-inch-wide lengths.)
Bring a small pot of water to a boil, add the salt and cook the broccoli briefly, 1 to 2 minutes. Drain, shock with cold water to stop the cooking, drain again and set aside.
Heat a wok over medium heat and add 2 tablespoon oil. Stir in 2 tablespoons sweet soy sauce, the chicken and 1 egg white. Stir constantly until the chicken is partially cooked and the egg white has set. Set this aside to rest.
Heat the wok over high heat and add 1 tablespoon oil. Add 1 egg, stir, then add the chicken. Remove the chicken when partially cooked and set aside. Add the remaining egg to the wok, stir, and add the rice noodles. Return the chicken mixture back into the pan. Stir and add the remaining tablespoon of soy sauce, the sweet soy sauce, oyster sauce and vinegar. Add the broccoli and stir to incorporate. Cook until the chicken is white and tender. Serve immediately.
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