If using dry navy beans, rinse them under cold water and soak them overnight in plenty of water. Drain and rinse before cooking. If using canned beans, skip this step.
In a large pot or Dutch oven, heat the olive oil over medium heat. Add the chopped onion and garlic, sautéing for about 4-5 minutes until the onion becomes translucent.
Add the diced carrots and celery to the pot, cooking for an additional 5 minutes until softened.
Stir in the dried thyme, bay leaf, and navy beans (whether dry or canned). If using dry beans, add the vegetable broth; if using canned beans, add enough broth to cover the beans and vegetables.
Bring the mixture to a boil, then reduce the heat to low. Cover the pot and let it simmer for about 60 minutes if using dry beans, or 20 minutes if using canned beans, until the beans are tender.
Remove the bay leaf. Using a wooden spoon, gently mash some of the beans against the side of the pot to thicken the soup.
Season the soup with salt and pepper to taste. Serve hot, garnished with fresh parsley if desired.