Sauté carrot, celery and leek in oil in nonstick saucepan until very soft, 8 to 10 minutes (add 1/4 cup water if necessary to prevent sticking). Add broth and potatoes; simmer until potatoes are almost tender, about 10 minutes.
Add green beans, tomato, squash, zucchini and salt; cook until tender, about 10 minutes.
Ladle soup into 10 soup bowls. Swirl 1 tablespoon of the pesto into each serving. Makes 10 servings.