Place finnan haddie in a large saucepan or soup kettle; pour boiling water on top. Spread onion over fish. Cover pan, bring almost to boiling point, reduce heat to very low and simmer gently for 20 minutes, or until fish is tender. Remove and flake fish, discarding any skin, bones and hard parts. 
Strain liquid, return to rinsed pot and simmer, covered, for 30 minutes.
Meanwhile, peel and boil potatoes until tender. Drain and mash thoroughly with butter, salt and pepper. Add to liquid in pot; stir to combine. 
In a small saucepan, or in the microwave, heat milk; add to soup pot and blend until smooth. Stir in flaked fish. Taste, and adjust seasonings if needed. Heat for 2 or 3 minutes, but don’t allow to boil.  Ladle into soup plates and garnish with chopped chives and a pat of butter, if desired. Makes 6 servings.