Add the parsley sprigs, celery, leeks, onions, and parsnips to a large (7-quart) soup pot and add enough water to cover vegetables (about 8 cups). Stir in 2 teaspoons salt and 1 teaspoon pepper; then simmer over medium-low heat for 1 hour.
Meanwhile, fry bacon in a large pan over medium-low heat until browned, about 30 minutes. Transfer bacon to paper towels to drain.
Remove the parsley from the soup, then add tomatoes, clam juice, white wine, carrots, potatoes, thyme, and bacon. Bring to a boil over high heat, then reduce to a simmer. Cook, covered, until potatoes and carrots are tender, about 15 minutes, then add clams. Simmer 15 minutes, or until clams open up. Discard any clams that do not fully open.
Remove the pot from heat. Season soup to taste with salt and pepper, and stir in chopped parsley. If desired, remove clams from shells before serving. Ladle soup into bowls, and garnish each with thyme sprigs (if using); serve with slices of crusty bread on the side.