In a small bowl, sprinkle the yeast over the warm water. Stir and allow to sit until the yeast is frothy, about 10 minutes.
In the bowl of a stand mixer fitted with the dough attachment or a large bowl, combine the water with activated yeast, butter, and egg.
Mix in the flour, sugar, cardamom, and salt until a dough forms. On a lightly floured surface, knead the dough until soft and smooth. If it is too sticky to handle, add a little more flour (just enough to remove the stickiness- don't add too much or it will create tougher rolls).
Place the dough back in the bowl, cover with plastic wrap or a towel, and allow to rise until doubled, about 1 hour.
Line two baking trays with parchment or lightly grease.
Divide the risen dough into 12 equal pieces. Roll each piece into a ball and place at least 3 inches apart on the prepared baking sheets. Cover with dish towels and allow to rise for another 30 minutes.
Preheat oven to 425˚F.
In a small bowl, beat the egg. Brush over the risen buns and bake in the preheated oven until golden, 10-12 minutes.
Allow the buns to cool for about 10 minutes before slicing in half and spreading with a thick layer of butter. Serve immediately.