Sauté the Vegetables: In a large pot, melt the butter over medium heat. Add the diced onion, celery, and garlic. Sauté for about 5 minutes until the vegetables soften.
Cook the Potatoes: Add the diced potatoes to the pot and stir in the flour. Cook for another 2 minutes to ensure the flour coats the potatoes and vegetables.
Add Broth and Clam Juice: Stir in the clam juice and chicken or vegetable broth. Bring to a simmer and cook for 10-12 minutes, or until the potatoes are fork-tender.
Add Clams and Dairy: Stir in the chopped clams, heavy cream, and milk. Combine well, and cook over low heat for 5-7 minutes to let the flavors meld together. Do not boil.
Season the Soup: Add the thyme, salt, and pepper to taste. Adjust the seasoning as necessary.
Serve: Ladle the chowder into bowls and garnish with fresh parsley. For an added touch of flavor and crunch, top with crumbled bacon if desired.