[I'm also Icelandic] when people say they eat "cod heads" they usually don't mean you eat the head whole, although it's also boiled for e.g. broth or stew. They usually mean that they eat the cheeks and tongue of the fish, and sometimes the eyes.
This is a delicacy in Iceland (gellur & kinnar) and I'm surprised you haven't heard of it., you've been missing out. Here's a video of a fishmonger (in Icelandic, but it mostly speaks for itself) extracting the two. Gellur (tounge) at around 1m30s, kinnar (cheeks) at 3m50s: https://www.youtube.com/watch?v=RcmHCoMQ01c
The cheek or other head tissue on the fish is usually the most delicious. On cods the cheeks are particularly big, but on most fish there's a small and tender cheek muscle you can easily get to.
Fun story: I was once at a wedding in Singapore where they served fish, and all the ethnic Chinese there were getting the whole fish including the head, but the waiters were serving all the foreigners (mostly Europeans) fillets. The natives were shocked and impressed when I asked for what they were having, and proceeded to eat edible parts of the head, including e.g. the eyes.
I had to explain that Iceland was a bit unusual as European cuisine goes, and much closer to the Chinese tradition of not needlessly throwing away useful food just because it looks odd.
