This is a lighter, brothy take on the Italian soup ribollita, which is also made with leftover bread. If using frozen peas, add them to the soup along with the bread.
In a large Dutch oven or heavy pot, heat oil over medium. Add onion, celery, and garlic and cook, stirring occasionally, until onion is translucent, 4 minutes. Season with salt and pepper. Add zucchini and thyme and cook until thyme is fragrant, 1 minute. Increase heat to medium-high, add broth and 1 cup water, and bring to a boil. Reduce heat and rapidly simmer 10 minutes. Add peas and cook until vegetables are tender, about 5 minutes. Remove thyme stems, stir in bread, and season to taste with salt and pepper. To serve, top with parsley.