Finely chop the onion and mince the garlic. Heat a large pot over medium heat, add a splash of oil, and sauté the onions for about 5 minutes until translucent. Stir in the garlic and cook for an additional minute.

Dice the carrots, celery, and potatoes, then add them to the pot with the onions and garlic. Cook for 8-10 minutes until the vegetables soften slightly.

Pour in the vegetable broth, bring to a gentle boil, reduce to a simmer, add bay leaves and thyme, and let it simmer for 20-25 minutes, or until the potatoes are fork-tender.

Slice the sausage and add it to the pot, or add the rinsed beans for a vegetarian option. Simmer for another 10 minutes to meld flavors.

Taste the soup and season with salt and black pepper. Stir in fresh parsley before serving.

Ladle the soup into bowls and garnish with additional parsley or croutons. Serve hot with crusty bread or pretzels.