In the bowl of a stand mixer, combine the flour, yeast, salt, and sugar.
Using a dough hook, mix the dry ingredients thoroughly.
Add the egg and the cooled Tangzhong.
Gradually pour in the milk, mixing until a sticky dough forms.
Incorporate the butter, one tablespoon at a time, ensuring each piece is fully blended before adding the next.
Knead the dough on medium speed for 10-15 minutes, until it passes the windowpane test and pulls away from the sides of the bowl.
Lightly oil a clean mixing bowl.
Shape the dough into a smooth ball and place it in the oiled bowl.
Cover with a tea towel or bowl cover and let it rise in a warm place for about 1.5 hours, until doubled in size.