Measure the flour, yeast, salt and sugar into the bowl of an electric stand mixer.
Mix the dry ingredients together using a dough hook.
Add the egg and the cooled Tangzhong.
Slowly add the milk until the mixture comes together into a sticky dough.
Add the butter, one tablespoon at a time. Wait for each tablespoon of butter to be fully incorporated into the dough before adding the next.
Continue kneading the dough on medium speed for about 10-15 minutes, or until the dough passes the windowpane test. (See Kitchen Notes below). By this stage, the dough should also be coming away from the sides of the bowl.
Lightly oil a large, clean mixing bowl.
Roll the dough into a smooth ball and place it into the mixing bowl.
Cover the dough with a clean tea towel or bowl cover, and place it somewhere warm for about 1.5 hours, or until it has doubled in size.