Heat butter in a saucepan, and sauté the onions, carrots and garlic, stirring frequently, for about 5 minutes. Remove from heat and slowly stir in the flour. Return to the heat and continue stirring for about 4 minutes, making a roux. Meanwhile begin heating the stock in a large stock pot. Wisk about two cups stock into the roux.
Add the diluted roux to the stock pot. Bring the stock to a boil, then reduce heat and simmer for 10 minutes. Add the fish to the stock pot and continue simmering for 15 minutes. Stir in the cheese and cream, simmering until the cheese melts, about 5 to 8 minutes.
The cheese will become incorporated into the chowder and you won't be able to distinguish it. Add salt and fresh pepper to taste. When reheating chowder, heat VERY slowly, DO NOT allow the cream to boil.