Put the flour in a big bowl.
Add sugar and yeast on one side of the bowl, and salt on the other.
Beat an egg, add 30g to the bowl, leave the rest for the egg wash later on.
Add the milk. Mix roughly, and start kneading either with a mixer or by hand until it becomes a smooth dough.
Add butter, and continue to knead again a smooth dough formed, ideally you see a thin membrane formed when you try to stretch the dough thin.
Leave the dough in a closed oven to prove for the first time for 45 mins until it doubles in size - I also leave a pot of lukewarm water in the oven. (Alternatively, cover with a cling film or damped towel, and leave it in a warm place.)
Press all the air out from the dough. Shape it round, leave it to rest for 15 mins covered.
Divide the dough into 4 pieces equally (each should be ~115g - alternatively, we made 2 normal size burger buns and 4 mini burger buns.) For each dough, press all the air out. Now it's the time to shape the dough - try to tuck the side of the dough to the bottom, roll the dough with your palm like a round ball. Leave it on the baking sheet.
Leave the dough balls in the closed oven for a second prove (or cover with cling film at a warm place), for around 30 mins.
Take the dough balls from the oven. Pre-heat the oven at 180°C.
Brush some egg wash right before putting the dough in the oven.
Bake in the oven for 12-15 mins until the buns are golden brown. Leave them on a rack to cool down completely before cutting them apart for burgers.