– 1 ½ pound fish heads, [0.7 kg] – 2 tablespoon olive oil – Juice of 1 lime – 4 clove garlic, sliced – 1 cup auyama (kabocha squash), (West Indian pumpkin or kabocha squash), diced, divided – 2 sprigs of cilantro, or parsley – 1 large carrot, peeled and diced – 1 cup potatoes, peeled and diced – 1 pound fish fillet, [0.45 k] cut into small pieces – 1 ½ teaspoon salt, (or more, to taste) – 1 teaspoon pepper (freshly-cracked, or ground), (or to taste)
In a deep pot mix the fish head (see notes), olive oil, lime juice, garlic cloves, and half of the auyama. Pour in 2.5 quarts [2.5 liters] of water. Boil covered over medium-high heat until the auyama has dissolved and heads are cooked and flaky (25 to 35 minutes). Remove from the heat and sieve to discard the solids. You can return any large pieces of cheek meat to the broth if you wish to dig it out.
Add the fish fillet to the pot and cook until it is cooked through (5-10 minutes). In the end, you should have about half the liquid you started with, if it's too little, add some more water and heat through, if it's too much, simmer some more to reduce it. This is not a thick soup, the liquid has the consistency of broth.