First, combine the whole milk and flour in a small saucepan, whisking until completely smooth with no lumps remaining. Place the saucepan over medium-low heat and stir continuously until the mixture thickens into a smooth, glossy paste similar to pudding. Once thickened, transfer it to a bowl and allow it to cool completely before using.
Meanwhile, combine the lukewarm milk, sugar, and active dry yeast in a large mixing bowl. Stir gently and allow the mixture to rest for 5–10 minutes until it becomes foamy and bubbly, indicating that the yeast is active.
Next, add the cooled Tangzhong and the egg to the activated yeast mixture, stirring until fully combined. Gradually add the flour and salt, mixing until a rough, shaggy dough forms and all of the flour is hydrated.
Transfer the dough to a stand mixer fitted with a dough hook or knead by hand. Gradually incorporate the softened butter, adding a little at a time while continuing to knead. Keep kneading until the dough becomes silky, smooth, elastic, and slightly tacky. It should pass the windowpane test when fully developed.
Place the dough into a lightly greased bowl and cover it with plastic wrap or a damp towel. Allow it to rise in a warm place for 45–60 minutes, or until doubled in size.
Gently punch down the risen dough to release excess air. Shape it into a tight log, making sure to create good surface tension. Carefully place the shaped dough into a well-greased Pullman loaf pan.
Cover the pan loosely and allow the dough to rise again until it reaches approximately ½–1 cm below the Pullman lid. This ensures the bread expands perfectly during baking without overflowing.
Preheat the oven to 175°C (350°F). Slide the Pullman lid closed and bake the loaf for approximately 35 minutes. If needed, uncover the loaf during the final few minutes to achieve a deeper golden colour on top.
Finally, remove the loaf from the oven and allow it to cool in the pan for about 10 minutes. Carefully remove it from the pan and transfer it to a wire rack to cool completely before slicing. Cooling completely helps maintain its soft texture and prevents the crumb from becoming gummy.