In a large pot, melt the butter over medium heat. Add the diced onion and cook until translucent, about 5 minutes. Stir in the minced garlic and cook for an additional minute until fragrant.
Add the diced carrots and celery to the pot, cooking for another 5 minutes until they begin to soften.
Stir in the cubed potatoes, fish stock (or chicken broth), bay leaf, thyme, salt, and pepper. Bring the mixture to a boil, then reduce the heat and let it simmer for about 15 minutes, or until the potatoes are tender.
Once the potatoes are cooked, stir in the heavy cream and bring the chowder back to a gentle simmer.
Add the cod pieces to the pot and cook for an additional 5-7 minutes, or until the fish is cooked through and flakes easily with a fork.
Remove the bay leaf before serving. Ladle the chowder into bowls and garnish with fresh parsley.