Heat the oil in a soup pot. Add the onions and sauté over medium-low heat until translucent.
Add the garlic and continue to sauté until both are golden.
Add the carrots, celery, and potatoes, along with just enough water to cover the vegetables (about 3 cups). Bring to a slow boil, then lower the heat and simmer gently, covered, until the vegetables are nearly tender.
Stir in the crushed tomatoes, optional wine, bay leaves, seasoning blend, and beans. Return to a simmer, then cover and simmer gently until the vegetables are done, about 15 to 20 minutes longer.
Add the green peas, parsley, and optional thyme or oregano. Adjust the consistency with more water as needed if the soup is too crowded, then season with salt and pepper. Discard the bay leaves and serve.