In a large Dutch oven or heavy-bottomed pot, heat butter over medium-high heat until frothy. Decrease heat to low, and add leek, yellow onion, celery, fennel, bay leaves and a big pinch of salt, and cook, stirring occasionally, until softened, about 10 minutes.
Increase heat to high, and garlic and incorporate into the vegetable mixture. Add wine and, and cook, stirring occasionally, until almost dry. Add stock, and bring to a boil. Reduce heat, and simmer for 20 minutes.
Season stock mixture to taste with salt and pepper. (Keep in mind that the oysters will add some more salt.) Add cream. Bring back to a simmer, and simmer for 20 minutes. Do not let boil.
Add thyme and oysters with liquor to soup. Taste and adjust seasonings if necessary; bring back to a simmer, and cook for 5 to 10 minutes. Remove from heat, and season to taste with salt, pepper, and hot sauce. Divide soup among serving bowls, and garnish with green onion, cheese, lemon juice, and fennel fronds, if desired.
Notes
Tip from Chef Jean-Paul: If you wanted to make this into a chowder, just add some potatoes and bacon.
Recipe by Louisiana Cookin' at https://louisianacookin.com/oyster-soup/