Trim the salmon to fit into your largest roasting pan, removing the head and most of the tail. Weigh the fish and calculate the cooking time at 30 mins per kg/13 mins per lb. Wash any blood from the body cavity. Season well inside and place in the pan. Set aside.
Heat oven to 160C/fan 140C/gas 3. Make the court bouillon. Place all the ingredients into a pan with 11⁄2 litres cold water. Bring to the boil, then simmer for 20 mins. Strain the liquor over the fish, cover tightly with foil and cook in the oven for 45 mins-1 hr.
Meanwhile, make the sauce. Sauté the peppers and shallot in the oil for 5 mins. Strip the leaves from the basil and chop the stems. Add the stems to the pan along with the vinegar, wine and seasoning. Simmer for another 10 mins or so, then season to taste. Tear most of the basil into pieces and scatter over the sauce, then set aside to infuse.
Remove the fish from the oven, uncover but leave in the liquor for another 15 mins, then carefully lift from the pan onto a board. Peel off the skin and, using the back of a table knife, scrape away the brown flesh as neatly as possible. Slide the whole fish onto a platter. Spoon some of the sauce on top, sprinkle with the remaining basil and put the rest into a bowl to serve.