Heat olive oil in a large pot over medium heat. Add onion, carrots, and celery. Cook for 5–6 minutes, until softened.
Stir in garlic, potatoes, zucchini, bell pepper, and corn. Cook for another 5 minutes.
Pour in vegetable broth. Add thyme, basil, paprika, salt, and pepper. Bring to a boil, then reduce heat and simmer 20 minutes, until vegetables are tender.
In a small bowl, whisk flour with 2 tablespoons of cream to make a slurry (optional, for a thicker soup). Stir into the pot.
Reduce heat to low, stir in cream, and simmer another 5 minutes. Add broccoli florets and cook just until tender, about 3–4 minutes.
Taste and adjust seasoning. Serve hot, garnished with parsley and Parmesan if desired.