Add all the ingredients into the mixer bowl except butter (for later use). You can whisk milk and the egg together beforehand to better incorporate all ingredients.
Knead on low speed to mix the ingredients well, then gradually raise the speed. Knead for 5 minutes.
When the dough begins to form a ball, do a windowpane test (see Note 1).
Add in unsalted butter, then continue kneading for 10 minutes. Do a windowpane test again (see Note 2).
Take out the dough from the mixer bowl and shape it into a ball.
Place it back into the mixer bowl, cover it with cloth or cling film and proof it for 1 hour (or until double in size) in room temperature.
Pat the dough to release air bubbles. Divide into 6 equal pieces and work on one piece at a time.
Shape each piece into a ball then pinch to seal the seams.
Cover the dough balls with a damp cloth or cling film and let them rest for 15 minutes.
Roll the dough into a rectangular shape then tuck and roll up the long side towards yourself.
Pinch to seal the seams then roll into a rope with a length of two and a half sausages.
Tuck in the rope end then swirl the dough rope around the sausage. Be sure to shape the buns tightly to maintain its form during the 2nd fermentation. Pinch to seal the ends. The front and back end should be on the same side, which is the bottom side of the bun.
Repeat the steps for the other dough pieces.
Proof for the 2nd time (about 1 hour or until the buns double in size).
Preheat the oven to 180°C.
Brush egg wash on the surface of the sausage buns.
Bake for 15-16 minutes.