Whisk the water, milk, and bread flour together in a small saucepan until smooth. Place over low heat and cook, whisking the whole time, until it thickens into a paste thick enough that the whisk leaves visible lines on the bottom of the pan,  about 4-5 minutes. Scrape it into a bowl and let it cool to room temperature before moving on, about 30 minutes.

While the tangzhong is cooling, combine all the other ingredients including the bread flour, dry milk powder, sugar, salt, yeast, milk and egg. Then add tang zhong once it is fully cooled. Mix by hand until it forms roughly into a dough ball, then move it to a floured surface.

This dough needs more kneading than a typical loaf because of the extra moisture from the tangzhong. If it is too sticky to knead, stretch the dough out and fold repeatedly. Dropping the dough onto the surface and pounding will also help. Half way through, add your butter and continue. Keep going until you can stretch a small piece thin enough to see light through without it tearing. If kneading by hand, this process may take up to 30 minutes.

Shape the dough into a ball, place it in a lightly greased, covered bowl, and let it rest for 60 minutes in a warm environment. If your oven has a proofing function, leave it it in as this works best. . It should look puffy,  it doesn't need to fully double.

Cover loosely and let the loaf rest for 40-50 minutes, until puffy and close to the rim of the pan.

Preheat the oven to 350°F. Brush the top with milk or an egg wash (1 egg beaten with 1 tablespoon cold water), then bake for about 30 minutes, until deeply golden on top. A thermometer inserted into the center should read at least 190°F.

Let the bread cool in the pan for about 30 minutes, then turn it out onto a wire rack and let it cool completely. Enjoy!