Makes 4 quarts, 6 to 8 servings
Heat olive oil in a 6-quart or larger soup pot over high heat. Add onions, carrots, and celery and cook for 2 minutes, stirring frequently. Add garlic, mushrooms, and parsley and cook for 3 minutes. Add stock, salt, and pepper. Cover and bring to a boil. Remove cover, reduce the heat to medium-low, and simmer for 12 minutes.
Add broccoli, zucchini, and yellow squash. Simmer 5 minutes.
Remove parsley sprigs and serve soup hot, garnished with the grated cheese, if desired.