Heat butter in a stock pot over medium heat and add potato, carrot, celery, garlic and onion. Cook for 5 minutes or until onions are translucent, but not brown.
Sprinkle flour over vegetables and stir. Continue cooking for another 5 minutes, stirring often.
Stir in fish stock, a little at a time and bring to a boil. Reduce heat and simmer for 5 minutes.
Add cream and bring to a boil again. Simmer for 5 minutes more. If thickness is to your liking, do not use the cornstarch mixture. If you would like the chowder a little thicker, add some of the cornstarch mixture, a little at a time, until you reach your desired thickness. If you are using heavy cream, you shouldn’t need much, if any. If you are using milk, especially skim milk, you may want to thicken it up a bit.
Once you have the thickness of the chowder under control, add the fish. Cook for just a few minutes, stirring only gently a time or two. Add salt and pepper as desired.
To serve, ladle chowder into bowls and garnish with chopped parsley.