1. Prepare the tangzhong: In a small saucepan, whisk 3 tbsp bread flour with 1/2 cup milk. Cook over medium heat, stirring constantly, until it thickens into a smooth paste. Remove from heat and let cool.

2. Activate the yeast: Warm 1/2 cup milk to about 110°F, add 1 tbsp sugar and the yeast. Let it sit until foamy, about 5–10 minutes.

3. Mix the dough: In a large bowl or stand mixer, combine bread flour, the rest of the sugar, salt, cooled tangzhong, yeast mixture, one egg, and softened butter. Knead until the dough is smooth and elastic, about 10–15 minutes by hand or 8 minutes in a mixer.

4. First rise: Transfer the dough to a greased bowl, cover, and let rise in a warm place until doubled in size, about 1–1.5 hours.

5. Shape the loaf: Gently deflate the dough, divide it into 3 or 4 equal pieces, shape each into a ball, and arrange them in a greased loaf pan.

6. Second rise: Cover the pan and let rise again until the dough reaches near the top, about 40–60 minutes.

7. Bake: Preheat the oven to 350°F (175°C). Brush the top with egg wash. Bake for 28–32 minutes until golden brown.

8. Cool: Remove from the oven and cool in the pan for 10 minutes, then transfer to a wire rack. Slice and enjoy!