In a mixer bowl, combine bread flour, sugar, salt, yeast, milk, and Tangzhong, leaving the unsalted butter for later use.
Knead the dough at a low speed to gently mix the ingredients for 15-30 seconds.
Gradually raise the speed, then knead for 5-8 minutes.
When the dough begins to form a ball, do a windowpane test (see Note 1).
Add in butter. Continue kneading for 10-12 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 until double in size (about 1 hour) at room temperature.
Take out the dough and check if it has properly proofed (see Note 3).
Pat the dough to release air bubbles.
Divide the dough in half and work on one piece at a time.
Flatten the dough and shape it into a rectangle.
Fold each side into the centre. Rotate the folded dough, gently flatten, and fold the other two sides.
Let them rest for 15 minutes.
Roll the dough into a rectangular shape. On the longer side, fold each side into the centre. Roll the dough to flatten it.
Starting from the short side, roll up the rectangular dough into a cylinder shape. Pinch to seal the seams and the ends.
Repeat for the other piece.
Place the loaves into a loaf pan. Let them proof for a 2nd time until double in size (about 1 hour).
Brush the loaves with egg wash.
Bake for 30-35 mins in a preheated oven at 180°C.