Cut the broccoli into lengths. Peel the tough stems and cut to the same size as the leafy portions.
Heat 2 tablespoons of the oil in a wok over high heat. Add the noodles and soy sauce and stir-fry for about 30 seconds. Push the noodles to the sides of the pan and add the egg. Stir the egg and noodles together and transfer to a serving platter.