Heat olive oil in a 5- to 6-quart pot over medium heat. Add onion, carrots, celery, and a pinch of salt. Cook for 7 to 9 minutes, stirring often, until the onion is translucent.
Add garlic, tomato paste, oregano, thyme, and red pepper flakes. Cook for about 1 minute, stirring, until the tomato paste darkens slightly.
Pour in 1 cup broth and scrape the pot, then add the remaining broth and diced tomatoes.
Add potatoes, green beans, and remaining salt. Bring to a gentle boil, then reduce to a steady simmer and cook uncovered for 12 to 15 minutes, until potatoes are just barely tender.
Stir in zucchini, cannellini beans, corn, and peas. Simmer for 7 to 9 minutes, until zucchini is tender and potatoes are fully soft.
Turn off the heat. Stir in lemon juice and parsley, then taste and adjust salt and pepper as needed.