Step 1In a large, wide soup pot, cook the onion in the oil over high heat for about a minute. Add the leek, celery, carrot, potato, parsley mixture and bay leaves. Turn the heat to medium and cook, stirring frequently, for 5 minutes. Add 1 cup of the broth and the mustard greens, toss with 2 teaspoons of salt and cook, covered, until the greens have wilted down, about 5 to 7 minutes.
Step 2Add the rest of the stock, bring to a boil, then simmer, covered, until the mustard is tender and mild, 25 to 35 minutes.
Step 3Add the spinach and arugula and cook until tender and bright green, about 3 to 5 minutes. Taste for salt and season with pepper.