Make the Tangzhong: Whisk 2 tablespoon bread flour, 2 tablespoon water, and 4 tablespoon milk in a saucepan over medium heat until it forms a thick paste. Transfer to a bowl and let cool.

Activate yeast: Mix 1 tablespoon active dry yeast with 1 cup lukewarm milk. Let rest 10 minutes until frothy.

In a stand mixer, combine 3 ½ cups bread flour, salt, and sugar. Add the tangzhong, yeast mixture, and egg. Mix on low, then increase to medium. Add butter one tablespoon at a time until dough is smooth and pulls away from the sides.

Shape dough into a ball, place in a greased bowl, cover with a damp towel. Let rise 1-2 hours until doubled in size.

Grease a 9x13 baking pan. Divide dough into 12 equal pieces (about 2 oz each), shape into balls, place in pan. Cover and let rise another hour until doubled.

Preheat oven to 350°F. Brush rolls with egg wash (2 tablespoon milk + 1 egg). Bake 20-25 minutes until golden brown.