01 - Slice off the top of each sourdough loaf and hollow out the center, leaving a thick shell. Set aside.
02 - Melt butter in a large pot over medium heat. Add onion, celery, and carrots, and sauté until softened and fragrant, about 5 minutes.
03 - Stir in flour and cook, stirring constantly, for 2 minutes to form a roux.
04 - Gradually whisk in reserved clam juice. Add potatoes, bay leaves, thyme, and parsley. Bring to a simmer and cook until potatoes are tender, 10 to 12 minutes.
05 - Reduce heat to low, stir in clams, heavy cream, and milk. Simmer gently for 5 to 7 minutes, stirring often, until creamy and heated through without boiling.
06 - Remove bay leaves. Season with salt and freshly ground black pepper to taste.
07 - Ladle hot chowder into prepared sourdough bread bowls and serve immediately.