In a small saucepan, whisk together 3 tablespoons of bread flour and 1/4 cup of whole milk over medium heat until it thickens into a paste. Let cool.

In a bowl, mix 1/2 cup warm milk, 2 teaspoons sugar, and 2 1/4 teaspoons active dry yeast. Let it foam for 5–10 minutes.

In a stand mixer, combine 3 cups bread flour, 2 tablespoons sugar, 1 teaspoon salt, 1 large egg, cooled tangzhong, yeast mixture, and remaining 1/4 cup milk. Mix with a dough hook until a dough forms.

Add 3 tablespoons of butter and knead for 10–12 minutes until smooth and elastic.

Transfer to an oiled bowl, cover, and let rise for 1 to 1.5 hours until doubled in size.

Punch down and divide into 3 equal pieces. Roll each into a rectangle and then into a log. Place in a greased loaf pan.

Cover and let rise again for 45–60 minutes.

Preheat oven to 350°F (175°C). Brush top with egg wash and bake for 28–32 minutes until golden.

Let cool before slicing.