Pour the stock into a pot and bring to a simmer. Add the oysters and their liquid and cook 1 minute, or until just cooked through. Remove the pot from the heat. Scoop the oysters out with a slotted spoon and set on plate to cool to room temperature before cutting them into 1/4" pieces. Refrigerate until needed.
Melt the butter in a pot over medium heat. Add the onion, celery and garlic and cook until tender, about 5 minutes. Sprinkle in the flour and mix well. While mixing steadily, slowly pour in the oyster-flavoured stock. Add the potatoes, bay leaf and tarragon, bring to a boil and then reduce heat to obtain a gentle simmer. Simmer for about 10 minutes, or until the potatoes are tender.
Stir in the oysters and milk or cream and simmer just until the oysters are heated through, about 2 to 3 minutes. Sprinkle servings of the chowder with parsley.