Wash fish bones well under running cold water. Snip off and discard gills from inside head if still attached, and break or cut all the bones into small pieces.

Melt the butter in a large saucepan over medium-high heat and sauté the onion, parsnip, carrot, potato, and celery root until they start to soften, this should take about 7 minutes. Add the fish heads and off-cuts, water, salt, peppercorns, and bouquet garni and heat to boiling. Reduce the heat to low and simmer gently, partially covered for 30 minutes.

Drain the stock through a colander lined with cheesecloth into another large pot, pressing and squashing the ingredients to extract the juices.

In the original pot add the strained stock. Return to heat and bring to a boil over medium-high heat. Boil until stock is reduced to about 6 cups, about 20 minutes. Use stock immediately or cool quickly in an ice bath and store up to 3 days in the refrigerator or 6 months in the freezer.