In a large pot bring a few inches of water to a boil. Drop spinach and asparagus pieces in water for a couple of seconds, remove and rinse with cold water. Set aside. Scramble eggs in a small cup and set aside.
Place butter in a large pot over medium heat. When it melts, add the celery, chicken, salt, pepper, and nutmeg. Brown chicken until just cooked through, then add spinach, mushrooms, zucchini and stock and bring to a boil.
Lower heat so that the soup is bubbling but not furiously. Mix the cheese with the eggs, then add the mixture to the soup in a steady stream, stirring constantly. You want to scramble the eggs, not just thicken the soup.
Cook, stirring occasionally, until the eggs are cooked and chicken is tender, 3-5 minutes more. Stir in parsley or other herbs, stir for 30 seconds, remove from heat and serve.
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