Heat olive oil in a large pot over medium heat. Add onion, carrots, and celery. Cook until softened.
Stir in garlic and cook until fragrant, about 1 minute.
Add zucchini, potato, green beans, tomatoes, broth, thyme, and oregano. Stir well.
Bring to a boil, then reduce heat and simmer uncovered for 20–25 minutes until vegetables are tender.
Stir in spinach or kale and cook until just wilted.
Season with salt and pepper. Ladle into bowls and sprinkle with fresh parsley.