1. Combine first 8 ingredients in large pot. Add water. Bring to boil, skimming surface occasionally. Reduce heat and simmer 20 minutes, skimming surface occasionally. Add fish fillets and cook until opaque, about 5 minutes. Remove fish fillets using slotted spoon and flake slightly, then set aside. Strain stock through fine sieve; do not press on solids. Return stock to pot and simmer gently until reduced to 5 cups, about 5 minutes.
2. Meanwhile, melt butter in heavy large saucepan over medium-high heat. Add 2 celery stalks, 1 carrot and 1 chopped onion and cook until vegetables begin to soften, stirring frequently, about 8 minutes. Mix in all remaining ingredients except sherry and rum. Add stock and bring to boil. Reduce heat and simmer 20 minutes.
3. Discard bay leaf. Mix in sherry and rum (or use sherry pepper sauce). Add fish, and serve immediately. (Note: The Bermudians add sherry peppers at the table.)