Heat the milk, in the microwave or a saucepan, until it is "fingervarm" (finger warm), meaning it should feel warm to the touch but not hot. Add your yeast and 1 tbsp of sugar, stir, and leave it for 5-10 minutes until the mixture starts to bubble up, meaning your yeast is alive. If using instant yeast that doesn't need to be activated, just combine the milk, yeast, and sugar in a bowl and move onto the next step.
Add the salt, remaining sugar (2 tbsp), cardamom, egg, and egg yolks to a large bowl and mix well. Once the yeast mixture has bubbled up a bit, add it to the egg mixture. Mix well.
Slowly add the flour and softened butter, mixing with a wooden spoon until the dough starts to come together.
Knead until smooth and elastic, about 10 minutes. Add more flour if the dough is too sticky; it should be soft and smooth, not too sticky nor too dry. Use a stand mixer if you would prefer!
Cover the dough with cling film or a clean, slightly damp dishtowel and place in the fridge overnight for 8 hours, or let rise at room temperature (if room temp is very cold wherever you are, put it in a warm place, i.e. under a light) for 1.5-2 hours or until doubled in size.
Once your dough has doubled in size, shape it into 16-20 balls and place on two baking sheets lined with parchment paper.
You can also crowd them all onto one pan if you would prefer buns that stick together as they bake. Cover and let rise for another 30 minutes. In the meantime, preheat your oven to 410 degrees F (210 degrees C).
Brush with egg wash (whisk together one egg and some water until there are no more gloopy egg streaks). Bake for 10-12 minutes. Check the bottom of the buns to see whether they are done - they should be golden brown and sound hollow when you tap them. If they're too pale, they'll need another minute or two.