Tangzhong:
Bread Dough:
Remove butter and egg from fridge to warm.
In a medium-heat saucepan, stir together tangzhong ingredients. Whisk constantly until it becomes a sticky, tacky, thick consistency. Remove from heat and allow to come to room temperature.
Add yeast to milk, allow to proof.
Mix flour, salt, and sugar together. Stir/knead in tangzhong, milk and yeast mixture, and egg. Once incorporated, knead in butter and knead for 5 minutes.
Form a ball, allow to rise in covered bowl for 1 hour or until doubled.
Punch down, separate into 9 even-size pieces, and shape them into balls. Place in greased 9"×9" pan, cover, and allow to rise for 1 hour or until doubled.
Wash with egg wash and bake at 350F (175C) for 28-30 minutes.
Serve (perhaps brushing with garlic butter).