Singed sheep’s head and jam made from the sheep’s head, either fresh or pickled in whey, are traditional foods in Iceland. Many types of fish and seafood are abundant in Iceland, with haddock, carpelin, herring, cod, plaice, lobsters, clams and shrimp being some of the most common varieties eaten.Fish is traditionally served boiled and accompanied by potatoes. Fish is often preserved by salting, smoking or drying.inged sheep’s head and jam made from the sheep’s head, either fresh or pickled in whey, are traditional foods in Iceland. Many types of fish and seafood are abundant in Iceland, with haddock, carpelin, herring, cod, plaice, lobsters, clams and shrimp being some of the most common varieties eaten.