This is a rich, flavorful, complex soup that — as with most soups — tastes even better for seconds the next day. I would consider adding only one thing — a few drops of pastis or other anise-based spirits. While it does have the licorice note of fennel already, I’ve always enjoyed an extra little tug of the flavor in the finish of cream-based seafood stews and chowders.
Bring 3 cups water to a boil in a large pot. Add lobster and cook until shells are red but meat is not yet cooked through, about 5 minutes. Remove with tongs to a rimmed baking sheet, save cooking liquid. When cool enough to handle, crack the shells over a bowl, saving as much juice as possible. Extract the tail and claw meat, chop it into 1- or ½-inch chunks, and reserve.
In a second large stockpot, melt the butter and add the onion, garlic, celery, carrots, and fennel over medium heat. Sauté the vegetables for about 10 minutes or until they are soft. Remove pot from heat and add brandy, return to heat and cook until brandy is almost evaporated. Add 1 cup of the lobster cooking liquid, the plum tomatoes and juice and bring the mixture to a simmer. Add the Donelan Nancie Chardonnay, chicken stock, bay leaves, thyme, and saffron. Bring the mixture to a simmer; cover it and cook for about 40 minutes.
After the 40 minutes is up, add the potato and cook until the potato is soft. Remove the bay leaves. Remove the soup from the stove and let it cool.
Just before serving, return the soup to the stove and slowly bring it to a gentle simmer. Stir in the heavy cream, cooked lobster, and season to taste with sea salt and ground white pepper. Immediately ladle into warm soup bowls.