Cook chopped bacon in a heavy pot over medium heat until crisp, 6 to 8 minutes. Transfer it to a paper towel–lined plate; leave about 1 tablespoon of fat in the pot.
Add butter, onion, and celery. Cook, stirring, until softened, about 5 minutes. Sprinkle in flour and cook 1 minute.
Slowly whisk in 1 cup clam juice and the broth until smooth, then add potatoes, bay leaf, thyme, and pepper. Bring to a gentle simmer and cook uncovered until the potatoes are tender, 12 to 15 minutes.
Stir in the remaining clam juice, reserved clam liquid, chopped clams, milk, and half-and-half. Heat gently for 5 to 7 minutes, stirring, until steaming; do not let the chowder boil.
Remove the bay leaf. Season with salt, ladle into bowls, and finish with bacon and parsley. Serve with oyster crackers.