In a small saucepan, combine 3 tablespoons of bread flour, 1/2 cup of water, and 1/2 cup of milk. Cook over medium heat, stirring constantly, until thickened, about 3-5 minutes. Allow to cool.

In a mixing bowl, combine 1/4 cup of warm water and 1 tablespoon of sugar, add 2 teaspoons of yeast, stir gently, and let sit for 5-10 minutes until foamy.

In a large mixing bowl, combine cooled Tangzhong, activated yeast mixture, 3 cups of bread flour, 1 teaspoon of salt, 1 beaten egg, and 3 tablespoons of melted butter. Mix until shaggy dough forms, knead for about 8-10 minutes.

Place kneaded dough into a greased bowl, cover, and let rise in a warm spot until doubled, about 1 hour.

Punch down the dough, transfer to a floured surface, shape into a loaf and place in a greased loaf pan, seam side down.

Cover with a damp cloth and let rise again until doubled, about 30-45 minutes. Preheat oven to 350°F.

Bake in preheated oven for 35-45 minutes until golden brown and sounds hollow when tapped.

Let cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.