Preheat the milk in a small pot and melt the butter in a small pan.
Pour the heated milk into a mixing bowl and sprinkle the dry yeast evenly over it. Wait 1 minute.
Add an egg and whisk it.
Stir in the lukewarm pre-dough and melted butter with a wooden spoon.
Pour the milk, yeast, egg, pre-dough, and butter mixture into the kitchen machine bowl.
Add sugar, salt, and half of the flour and mix it with a wooden spoon until the ingredients are well combined.
Then let your kitchen machine (use a dough hook) get to work.
Add the rest of the flour as it kneads and let the device combine it into a dough.
The dough is ready as soon as it separates from the bowls surface (approx. 5 minutes).
Take a clean bowl with a lid and coat it with a teaspoon of oil. Pour the dough into the bowl and close the lid.
Now the dough has time to rest for an hour at room temperature to double its volume.
Sprinkle a suitable work surface with a little flour and knead the dough there briefly to let the air out.
Divide the dough into 9 equal-sized pieces and form 9 little buns.
Place the buns on a baking sheet lined with baking paper.
Let them rise at room temperature for another 30 minutes until they have significantly increased in volume.
Now preheat the oven to 320 °F / 160 °C (circulating air) while whisking one egg yolk and one teaspoon of milk.
Brush the buns with the egg-milk mixture.
Bake for 10-15 minutes until golden brown.
Let the buns cool after baking.