In a stockpot, Dutch oven, or another large heavy pot, heat the oil over medium heat. Cook the onion and carrot until they begin to brown and release their juices, about 5 minutes.

Add the fish heads and bones, celery, parsley, peppercorns, salt, and water.

Bring almost to a boil, then reduce the heat and simmer, partly covered, for 30 minutes.

Strain and reserve the stock, discarding the solids.