Bring stock to boil in a large pot. Add carrots, leek, and celery. Simmer 15 minutes.
Add cauliflower, green beans, and tomatoes. Simmer 10 minutes.
Add zucchini and simmer 5 more minutes. Season generously.
Make pistou: pound garlic and a pinch of salt in a mortar. Add basil leaves gradually, pounding to a paste. Work in olive oil tablespoon by tablespoon. Stir in finely grated Parmesan.
Remove soup from heat. Ladle into wide bowls.
Place a generous tablespoon of pistou in each bowl. Stir at the table.
Serve with extra Parmesan and a drizzle of good olive oil.