Whisk together bread flour, whole milk, and water in a saucepan. Cook over medium-low heat until the mixture becomes glossy and thick, about 5 minutes, and a line forms at the bottom of the pan when you drag a spoon through it. Transfer the tangzhong to a bowl and let it cool. This will yield at least 200 g of tangzhong.
In the bowl of a stand mixer, using the whisk attachment, combine dry ingredients, taking care to put the salt and yeast on separate sides of the bowl. Mix briefly on speed 2 to combine well.
Add wet ingredients. Change the attachment to the dough hook. Continue to run the mixer for about 3 minutes, or until a shaggy dough forms. Turn off the mixer and let the dough rest for 10 minutes.
Run the stand mixer on speed 4 for 5 minutes. Add butter to the mixing bowl. Run the stand mixer for another 10 minutes, until the dough is smooth, elastic and tacky. The dough should pass the windowpane test (check the handy tips).
Shape the dough into a ball and let it rest for 10 minutes. Transfer to a greased bowl, cover, and leave in a warm location for 45-60 minutes, until doubled in size.
Punch down the dough to collapse it. Turn the dough out onto a lightly floured surface. Using a bench scraper and scale, divide into three equal portions by weight. Shape each piece by stretching the edges and folding them inward to form a smooth ball. Cover and rest for 15 minutes.
Using a rolling pin, roll each piece into a rough rectangle, measuring 8 by 5 inches. Fold the dough into thirds, as if you are folding a letter. Rotate the folded dough 90º and then lightly roll it out again into a 2 by 8 inch strip. Starting from the short side, roll the dough tightly into a log, as if you are rolling up a sleeping bag. Pinch the seam closed.
Butter the bottom, sides, and lid of a Pullman pan with butter. Place the three logs seam-side down in the pan with the spirals facing inward. The dough rolls should be touching each other. Gently level out the dough rolls with your hand. If you are seeking a square loaf, cover and proof until the dough is about 75-80% the height of the pan, about 35-70 minutes. Preheat the oven to 410ºF. After proofing, butter the lid and slide it onto the pan. If you are seeking rounded domes (yamagata), cover and proof until the dough is about 85-90% the height of the pan, about 50-70 minutes. Preheat the oven to 385ºF. Do not use the lid.
For the square loaf: bake the bread for 27 to 30 minutes at 410ºF. For the rounded dome: bake the bread for 30 minutes at 385ºF.
After removing the pan from the oven, immediately tap the pan firmly once or twice. Remove the lid and unmold the bread. Cool completely on a wire rack for at least 2 hours before slicing.