Doughnut is not a specific Icelandic pastry, it belongs to the food culture of Northern Europe: Fattigmann in Norway (Poor Mans’), Merveilles in France (Marvels), Chrust in Poland (crunchy), and as well in North Germany (krapfen), South Sweden (klenäter) and Denmark (klejner). It has been known since the middle ages under different shapes and way of cooking; boiled, fried or even pan-fried. The originality of the Icelandic kleinur (the name comes from "klein" in German, small) is the way it is twisted.
The wheat dough is flattened and made with eggs, buttermilk, butter, sugar, milk and spiced with vanilla and cardamom. Then, smaller rhomboid pieces are made and finally a hole is cut in the middle. To make a kleina (sing. of kleinur) twist one end through the hole to have the right shape.
Kleinur is one of the oldest pastry registered in a recipe in Iceland, by the end of the 18th century, but it seems to be even older: to cut the dough in the right shape, one needed a "kleinujárn" (kleinur cutter) and some have been found made out of whale bone as it was rather usual to use since metals were scarce.
Kleinur was used to be baked for Christmas, since it was quite exceptional at collecting frying fat and the ingredients. It is still a strong tradition in Icelandic homes both in the countryside and in town to bake kleinur now at any time of the year, and the pastry is one of the favourite pieces to accompany coffee or buffet for special occasions. Tradition belongs to grandmothers. While younger people are used to buy the industrial ready-to-eat kleinur on the market. Sheep fat (tólg) was used to deep fry and that has more or less disappeared.