In a small bowl, sprinkle yeast over the warm milk and stir briefly to combine. Let sit until frothy, 5-10 minutes.
In the bowl of a large stand mixer fitted with a dough hook, combine the flour, sugar, cardamom, and salt.
Add the frothy yeast with milk, egg, and butter.
Mix until a dough comes together.
On a lightly floured surface, knead the dough until smooth and elastic. Cover with a kitchen towel and let rise for 1-2 hours.
Preheat oven to 375˚F (190˚C). Line a baking sheet with parchment or lightly grease.
Separate the risen dough into 12 equal pieces.
Form each piece into a ball and arrange 2 inches (5 centimeters) apart on the prepared baking sheet.
Cover with towel and let rise until puffed, about 30 minutes.
In a small bowl, whisk together the egg and 1 tablespoon (15 milliliters) milk.
Brush the egg milk mixture evenly over the buns.
Bake the buns in the preheated oven until golden brown, about 15 minutes.
Transfer to a wire rack and allow to cool to room temperature.