Heat the oil in a large pot over medium heat. Add the onion and cook until the onion is translucent.
Add the garlic and cook another minute.
Add the leeks, celery, and carrots. Cook until they start to soften slightly
Add the stock and parsley. Raise the heat to high, bring to a boil. Once the soup has come to a boil, reduce the heat to medium-low and simmer covered for 20 minutes.
While the soup simmers, cook the pasta according to package instructions and set aside until needed.
Add the zucchini and simmer another two minutes.
Add the spinach and simmer an additional two minutes.