Prepare the bread bowls: Preheat oven to 375°F (190°C). Slice the top 1 inch off each sourdough loaf horizontally. Carefully hollow out the inside bread, leaving a substantial 1-inch thick wall to create a sturdy bowl. Lightly toast the hollowed-out bowls in the oven for 10-12 minutes until slightly firm.

Sauté aromatics: In a large heavy-bottomed pot or Dutch oven, melt the butter over medium heat. Add the diced onion and celery. Cook until softened and translucent, about 5-7 minutes. Do not brown.

Create the roux and add liquid: Sprinkle the flour over the vegetables and cook, stirring constantly, for 1 minute. Slowly whisk in the clam juice/broth until smooth. Bring the mixture to a gentle simmer, stirring occasionally, until it begins to thicken slightly.

Simmer the potatoes: Add the diced potatoes and dried thyme to the pot. Season with salt and pepper. Reduce heat to low, cover, and simmer for 15-20 minutes, or until the potatoes are tender.

Finish the chowder: Stir in the heavy cream and the minced clams. Heat through gently for about 5 minutes, taking care not to boil the mixture once the cream is added. Taste and adjust seasoning as needed.

Serve immediately: Ladle the hot clam chowder generously into the toasted sourdough bread bowls. Garnish with fresh chopped parsley and serve with the reserved bread removed from the center for dipping.