In an 8- to 10-quart pan over high heat, bring broth to a boil.
Meanwhile, cut skin from butternut squash. Cut squash, carrots, potato, and celery into 1/2-inch cubes.
Add butternut squash, carrots, potato, celery, onion, and garlic to boiling broth. Cover, return to a boil, then reduce heat and simmer 10 minutes.
Meanwhile, cut zucchini and red bell pepper into 1/2-inch cubes.
Add zucchini, bell pepper, basil, and beans to broth. Cover and return to a boil over high heat. Reduce heat and simmer until all vegetables are tender when pierced, about 20 minutes longer.
Stir 1/4 cup pistou into soup, then ladle soup into bowls or mugs. Add salt and pepper and more pistou to taste.