Whisk 28 g bread flour, 120 ml whole milk, and 120 ml water in a small saucepan. Cook over medium-low heat, stirring constantly, until smooth and thickened to approximately 149–158°F (65–70°C), then cool until lukewarm.

Combine the cooled tangzhong with the lukewarm milk, egg, sugar, instant yeast, 360 g bread flour, and salt. Mix until a shaggy dough forms.

Knead with a mixer for 8–10 minutes or by hand for 12–15 minutes, adding the softened butter gradually. The dough should become smooth, elastic, and slightly tacky.

Place the dough in a lightly greased bowl, cover, and let it rise in a warm place for 60–90 minutes, or until doubled.

Gently deflate the dough and divide it into three equal pieces. Shape each piece into a smooth oval or short log and arrange them side by side in a greased 9 x 5-inch loaf pan.

Cover the pan and let the dough rise for 30–45 minutes, until puffy and approximately 1 inch above the rim.

Heat the oven to 350°F (175°C), brush the loaf with milk if desired, and bake for 30–35 minutes. Tent loosely with foil if the top browns too quickly, and bake until the center reaches approximately 190–195°F (88–91°C).

Cool the loaf in the pan for 5–10 minutes, then transfer it to a rack. Let it cool completely before slicing so the crumb can finish setting.