In a large pot, cook the chopped bacon over medium heat until crispy. Remove the bacon and set aside, leaving the drippings in the pot.
Add the diced onion and celery to the pot. Sauté for about 5 minutes, or until the onion is translucent.
Stir in the diced potatoes, clam juice, and reserved clam juice. Bring to a boil, then reduce heat and simmer for 15-20 minutes, or until the potatoes are tender.
Add the heavy cream, milk, chopped clams, dried thyme, and cooked bacon back into the pot. Stir well and heat through, but do not boil.
Season with salt and pepper to taste. Serve hot, garnished with fresh parsley.