You can be inspired by the French soup bouillabaisse, or some similar (of course you don’t have the same fish). It is one of my favourite fish soup. Maybe you will need to add more fish, the bones are not enough to make the soup tasty enough, it is a full meal on its own.
I have made sauce with shrimps heads, delicious! I guess fish carcass will give excellent result.
I am not an expert in Malaysian cooking, they make good use of fish heads cooked in curry. More about it here.
I make stock with salmon carcasses and heads. Fish stock is different from that made from meats. It doesn’t benefit from long simmering, but does ok with reduction after you remove the bones. For one carcass including the head, I fill the stock pot maybe halfway up and simmer on low heat for about 20-30 minutes, then I strain it in a collander to remove the bones, pressing to get all of the liquid out of the head/bones. Simmer to reduce until the flavor is strong enough. This makes about four quarts of stock, which I freeze up in individual quart containers and use it for fish soup, risotto, or my favorite concoction:
1 lb cubed fish steaks. Fish stores often offer a great deal on fish trim at a low price.
Onion, garlic, and whatever you like, chopped finely (“mirepoix”)
1 jar of broad beans, preferably Italian “gigantes”/butter beans (or even better, fresh broad beans, like “cranberry” beans).
1 quart fish stock.
Salt, pepper, herbs to taste
Saute the mirepoix in olive oil. Add the beans and simmer until they’re tender. Add the fish and simmer briefly until it’s just cooked. Season and serve forth.
(User seamunky suggests some bacon; you can fry it before adding the mirepoix)
If you like seafood sinigang, you can easily make the seafood sinigang using Mama Sita’s or Knorr’s tamarind soup mix which is essentially sinigang mix. You can buy the mix at the Asian store for $.75-$1. 00 . They often go on sale for .50 cents at which time,I usually pick up 10 if not 20 pouches to stock in the pantry. I follow instruction and usually add tomatoes, extra cider vinegar and hot pepper as we like it spicy, usually add , garlic, ginger and spring onion as well. For the seafood, tilapia fillet together with shrimp are often our choice. Prior to serving, I add a bunch of Ong Chay ( water spinach ) but if not available , spinach will do. During the summer till Fall, when we catch rockfish from our dock, I use the fish head and carcass after my son fillet the fish to make stock for paella. This fish stock also works great but even when I do not have stock, the mix is really good by itself. I know a lot of filipinos who now just use the mix.
Her in NYC they actually sell the carcass for about 99 cents per pound. I will by about 3 or 4 pounds, take a grapefruit teaspoon and scrape off all of the meat. I end up with about a pound and half of salmon. I then treat it like a ceviche with lime and orange juice, a few drops of sesame oil and a couple of red pepper flakes. I serve it with toasted rounds of baguette and top it off with some chopped red onion. Unfortunately in my house it is a first course for the five of us, and I never seem to make enough for leftovers for me!
I am planning to make what the fishermen used to do, cook the fish for perhaps a minute, scrape off all the meat for later, then simmer the carcass for half an hour (and now I realize one is too little), then add aromatics, tomatoes, shrimp, cod, scallops, saffron (all are stuff I have readily at home) and herbs. And maybe a tiny bit of potatoes. A mix between cioppino and bouillabaisse, I guess.
I made the bouillabaise-cioppino hybrid soup. I didn’t have scallop on hand- just the carcass, shrimps and cod fillet. It tasted pretty good. I think I could use more than a carcass. Or I added too much water.
I put the cod fillet in at the end. But if I am to make the soup again, I will saute the cod elsewhere and add to the soup when the soup is already in a bowl. Cooking the cod in the soup make the cod really bland, and eventually overcooked in the hot soup.
I have tried using the fillets of fresh red mullet and mackerel, simmered for 5-7 minutes in the soup before serving instantly. Mackerel has a stronger character turned out more suitable than mullet. On the whole, the soup was very good and worth the trouble. I wanted to add mussels, but due to the snow transport problem, there was nothing in the shop.
Using 20+ heads, I have made 6 big bowls of soup, pretty economic! Now I need to wait several months to collect enough heads for my next soup.