Step 1: Making the Tangzhong (Water Roux)

1. In a small saucepan, whisk together the bread flour, water, and milk until smooth.

2. Cook over medium-low heat, stirring constantly, until it thickens into a paste (about 2 minutes).

3. Remove from heat and let it cool to room temperature.

Step 2: Making the Dough

4. In a large mixing bowl, combine bread flour, sugar, salt, and instant yeast.

5. Add the warm milk, egg, and cooled Tangzhong. Mix until a dough forms.

6. Knead the dough for about 10 minutes (by hand) or 5 minutes (using a stand mixer with a dough hook) until smooth.

7. Add the softened butter and continue kneading for another 5-7 minutes until the dough becomes elastic and smooth.

8. Cover the dough and let it rise in a warm place for 1 hour, or until doubled in size.

Step 3: Shaping the Pai Bao Rolls

9. Punch down the risen dough and divide it into 8-10 equal portions.

10. Roll each portion into a smooth ball or oval shape.

11. Arrange them closely together in a greased loaf pan or baking tray, leaving a little space for expansion.

12. Cover and let them rise again for 45 minutes.

Step 4: Baking

13. Preheat the oven to 350°F (180°C).

14. Brush the tops of the rolls with the egg wash.

15. Bake for 18-20 minutes until golden brown.

Step 5: Cooling and Serving

16. Let the rolls cool slightly before enjoying them warm.