This soup is traditionally prepared in giant iron pots set over an outdoor fire. We used perch, but any firm-fleshed white fish such as cod or red snapper works just as well.
Melt 1/4 cup butter in a 16-quart stockpot over medium heat. Add onions; cook, stirring occasionally, until they are soft and translucent, about 15 minutes.
Add fish stock to pot. Place peppercorns and allspice on a small piece of cheesecloth, and tie into a pouch with kitchen twine. Add spice sachet to pot, tying one end of twine to handle of pot for easy removal. Raise heat, and bring stock to a boil. Add carrots and potatoes, and return to a simmer. Cook until vegetables are tender, about 25 minutes more. Stir in 3 tablespoons salt.
Add fish pieces to pot. Reduce heat; simmer until fish is cooked through and opaque, about 3 minutes.
Stir in remaining 1/2 cup butter and heavy cream. Continue cooking until soup is heated through, but do not allow it to boil, as it will separate. Remove spice sachet. Stir in dill and chives, and season with salt and pepper.
If you are cooking for ten to twelve people, reduce the amount of each ingredient by half.