In a large saucepan, heat oil over medium heat. Add onion, garlic and mushrooms. Cook, stirring occasionally, for 5 minutes.
Add broth, potatoes, carrots and salt. Bring to a boil. Reduce heat to medium, cover, and simmer for 5 minutes.
Add thyme, asparagus, zucchini, beans and red-pepper flakes. Cover and cook for an additional 5 minutes.
To serve, spoon into bowls and top each with 1 tablespoon shaved Parmesan cheese. Makes 6 servings.