Don't boil the fish!
This is an old Colonial recipe, from the days before hifalutin' words for technique like "poach" and "simmer" had entered the lexicon of everyday cooks.
When you see a mention of boiled fish in an old Yankee letter or book, it refers to salmon, cod, or other large fish poached in water or in a mildly-seasoned court-bouillon. Boiling a delicate piece of fish is a sure way to make a mess of it.
The best tool is a fish poacher: an oblong stainless pot that covers two burners and is long enough to fit about a 2.5 pound fillet. The pot has an insert that you set the fillet on, so you can easily lift it out when it's finished.