In a wok or a large nonstick skillet, heat the oil over medium-high heat. When the oil is lightly smoking, add the scallion whites, ginger, and garlic, and cook for 30 to 45 seconds. Add the zucchini, carrots, broccoli, and mushrooms, and cook for 4 to 5 minutes, using a spatula to stir the vegetables throughout. Add the chicken and continue cooking for 2 to 3 minutes, until the pieces are no longer pink. Stir in the rice and soy sauce, and cook for another 5 minutes, allowing the rice to get crispy on the bottom. Create an empty space in the middle of the pan and add the eggs. Use a spoon or the spatula to quickly scramble the eggs until light and fluffy, then stir them into the rest of the ingredients. Serve garnished with the scallion greens.