In a small bowl, sprinkle the yeast over the lukewarm milk. Stir to combine, then allow to sit until frothy, 5-10 minutes.
In the bowl of a stand mixer fitted with a dough attachment or a large bowl, stir together the flour, sugar, cardamom, and salt.
Mix in the yeast with milk, egg, and melted butter to form a light, loose dough.
Knead on a lightly floured surface until soft and smooth. If too sticky, add a little more flour. (be careful not to add too much flour, just enough to handle). If too dense and crumbly, add a little more milk. Transfer the dough into a greased bowl, turning to coat, cover, and allow to rest until doubled, about 1 hour.
Preheat oven to 375˚F (190˚C). Line two baking sheets with parchment or lightly grease.
On a lightly oiled surface, divide the dough into 12 equal pieces. Roll each piece into a smooth ball. Arrange on the prepared baking sheets about 2 inches (5 cm) apart, cover, and allow to rest until puffed, about 30 minutes.
In a small bowl, whisk together the egg and milk. Brush over the tops of each roll. Bake in preheated oven until golden, about 15 minutes.
These rolls are best served the day they are made.