In a 5- to 6-quart pan over high heat, bring broth to a boil.
Meanwhile, trim and discard tough dark green tops and root ends from leeks. Cut leeks in half lengthwise and rinse well under running water, flipping layers to release grit. Thinly slice leeks crosswise. Trim ends from sugar snap peas and remove strings; rinse and drain snap peas.
Stir pasta into boiling broth, then reduce heat and simmer for 5 minutes.
Add leeks, peas, and beans to pasta. Return to a boil over high heat, then reduce heat and simmer, covered, until pasta is tender to bite, about 2 minutes longer.
Stir in spinach, basil, and mint. Cook, covered, just until greens are wilted, about 1 minute.
Ladle soup into bowls. Add parmesan cheese to taste.
Wine pairing: The vegetables in the soup call for a crisp, grassy Sauvignon Blanc.
Note: Nutritional analysis is per serving.