Melt 1/4 cup butter in a saucepan over low heat. Add onions, celery, and carrots and cook until softened, about 20 minutes. Add broth, potatoes, and bouquet garni. Simmer until potatoes are softened but not squishy, about 20 minutes more. Add halibut and simmer soup for 5 minutes.
Melt remaining 3/4 cup butter in another saucepan over medium heat. Add flour and whisk until smooth. Add cream and whisk constantly until thick and smooth, about 15 minutes. Blend roux into the soup. Remove bouquet garni just before serving and stir in dry white wine and pepper.
