For the bülla, whisk egg and sugar, then add yeast, butter, flour, salt, cardamom and milk to make a firm dough.
Let rise, then divide in half. Roll out each part 1/2 cm thick. Brush with softened butter, sprinkle with granulated sugar and cinnamon, fold and cut into 2 cm wide strips.
Twist spirals and shape into doughnuts. Let rise for 15 minutes, brush with egg and bake at 200 °C for about 15 minutes.