In a small bowl, combine warm milk and sugar.
Add the active dry yeast and let it sit for 10 minutes
Flour Paste: In a small pan, whisk together flour, milk, and water, until it turns into a paste. Remove from heat and let it cool.
In a large mixing bowl, add flour and salt.
Add the tangzhong, yeast mixture, sugar, and egg. Mix.
Knead the dough with a mixer and a dough hook.
Add the softened butter in small pieces and continue kneading until the dough is smooth.
Shape the dough into a ball and place it in a greased bowl.
Cover and let it rise in a warm place for 2 hours.
Punch down the dough and divide it into four equal pieces.
Roll out each piece into an oval, then fold the top and bottom edges toward the center.
Flatten with a rolling pin, then roll it up tightly into a log. Repeat 3x.
Cover and let it double in size.
Add logs to a bread pan.
Preheat oven to 350°F .
Brush the top of the dough with egg wash.
Bake for 25–30 minutes, until golden brown.