While the rest of Denmark is aptly represented in terms of local specialties, the closest Zealand gets is probably the famous smørrebrød, meaning buttered-bread, which has its origins in Copenhagen. These open faced sandwiches of rye bread and butter, comes with as many as 250 different toppings, and are usually finished by some elaborate decorations. Smørrebrød is usually eaten at lunch.
Further south, on the island of Møn the local specialty is bidesild chewy herring and is herring that has been pickled in brine over several years, and is served with bread and fat.
