Stir the active dry yeast into the warm tangzhong and let it sit until it begins to bubble and pop, about five minutes.
1 tablespoon active dry yeast
In the bowl of a stand mixer fitted with a dough hook, combine the tangzhong with the remaining dough ingredients. Mix on medium speed until a smooth, elastic dough forms, 12 to 15 minutes. The dough should feel smooth and slightly tacky.
2½ cup bread flour, ¼ cup nonfat dry milk powder, ¼ cup granulated sugar, 1 teaspoon kosher salt, ½ cup whole milk, 1 large egg, 4 tablespoon unsalted butter
Shape the dough into a ball and place it in a large bowl lightly greased with butter. Cover and let it rise in a warm place until puffy, about one to one and one-half hours. The dough will puff but not fully double in size.
1 tablespoon unsalted butter
Gently deflate the dough and divide it into three equal pieces (about 230 grams each). Working with one piece at a time, flatten it into a five by seven-inch (12.7 x 17.8 cm) rectangle. Fold the short ends inward like a letter, then flatten again into a four by six-inch (10.2 x 15.2 centimeter) rectangle. Starting from a short end, roll it into a tight log.
Arrange the logs seam-side down in a lightly greased nine by five-inch (22.9 x 12.7 centimeter) shokupan, placing them side by side.
Cover and let rise until noticeably puffy, 40 to 50 minutes. Toward the end of proofing, preheat the oven to 350°F (176°C).
Brush the top of the loaf with milk. For a perfectly square loaf, place the lid on the pan before baking.
Bake for 25 to 30 minutes, or until deeply golden brown and an instant-read thermometer inserted into the center registers at least 190°F (88°C).
Let the loaf cool in the pan for ten minutes, then transfer it to a wire rack and cool completely before slicing.