Prepare the Tangzhong: In a small saucepan, whisk together the water, milk, and bread flour until smooth. Place over low heat and cook, whisking constantly, until the mixture thickens and the whisk leaves lines on the bottom of the pan, about 3 to 5 minutes. Remove from heat and transfer to a small bowl to cool to room temperature.

Mix the Dough: In the bowl of a stand mixer fitted with the dough hook attachment, combine the cooled tangzhong, bread flour, dry milk, sugar, salt, instant yeast, warm milk, and egg. Mix on low speed until a rough dough forms.

Knead the Dough: Increase the mixer speed to medium and knead the dough for about 10 minutes, until it becomes smooth and elastic. Add the melted butter, a little at a time, and continue kneading until fully incorporated and the dough passes the windowpane test.

First Proof: Shape the dough into a ball and place it in a lightly greased bowl. Cover with plastic wrap and let it rise in a warm, draft-free place until doubled in size, about 1 hour.

Shape the Dough: Punch down the dough to release air bubbles. Turn it out onto a lightly floured surface and divide it into 3 equal pieces. Roll each piece into a ball, cover with a damp cloth, and let them rest for 15 minutes.

Form the Loaf: Roll each dough ball into an oval shape, then roll up tightly into a log. Place the logs into a greased 9x5-inch loaf pan, seam side down. Cover with plastic wrap and let the dough rise until it reaches about 80–90% of the pan’s height, approximately 1 to 1.5 hours.

Preheat the Oven: Preheat your oven to 350°F (175°C).

Bake the Bread: Brush the top of the loaf with an egg wash (1 beaten egg with 1 teaspoon water). Bake in the preheated oven for 30 to 35 minutes, until the bread is golden brown and sounds hollow when tapped on the bottom.

Cool: Remove the bread from the pan and let it cool on a wire rack before slicing.