Cook the bacon in a large pot over medium heat until crisp, then remove with a slotted spoon and set aside, leaving the fat in the pot.
Add the onion and celery to the pot, cooking until they soften, about 5 minutes.
Stir in the garlic and cook for another minute until fragrant.
Add the potatoes, stock, thyme, and bay leaf to the pot. Bring to a boil, then reduce to a simmer. Cook until potatoes are tender, about 15 minutes.
Add the fish pieces to the pot, simmer gently until the fish is just cooked through, about 5 minutes.
Reduce heat to low, pour in the cream, and stir. Let the chowder heat through but do not let it boil.
Season with salt and pepper to taste. Remove the bay leaf.
Serve hot, garnished with the reserved bacon and fresh parsley.