Heat 2 tablespoons olive oil in a Dutch oven or large pot over medium heat. Add 1 diced onion. Cook until soft and translucent, about 3 to 5 minutes.
To the pot, add 3 cut carrots, 3 cut celery stalks, 3 minced garlic cloves, 1½ teaspoons salt, and ¼ teaspoon freshly ground black pepper. Cook about 3 minutes, stirring occasionally.
Then, add 2 bay leaves, 1½ teaspoons finely chopped thyme, 1 can of tomatoes, and 6 cups broth. Stir to combine and bring to a boil over medium-high heat. Reduce the heat to a simmer and cook for 15 minutes.
Once simmered, add 8 ounces cut zucchini and 4 ounces cut green beans. Simmer until crisp-tender, about 15 more minutes. Then add, 1 cup frozen peas and 1 cup corn kernels. Cook for 5 more minutes.
Remove and discard bay leaves. Taste and season with more salt as needed.
Garnish with fresh parsley and serve.