Tangzhong:

Cup of Yum
1. In a small pot, mix together the 1/4 cup (33 grams) bread flour, 1/4 cup (60 milliliters) milk, and 1/4 cup (60 milliliters) water over medium heat using a small rubber spatula.
2. Continue to mix and fold until the mixture reaches a thick, pudding-like consistency.
3. Remove from heat and allow to cool to a lukewarm temperature.

To make the Shokupan:

1. In a small bowl, sprinkle the yeast over the 3/4 cup (177 milliliters) lukewarm milk. Mix together and allow to sit at room temperature until frothy, about 10 minutes.
2. In the bowl of a stand mixer fitted with a dough hook or a large bowl, combine the bread flour, sugar, and salt.
3. Mix in the lukewarm Tangzhong mixture from the pot and the frothy yeast with milk.
4. Mix in the softened butter until the dough completely comes together. It should be smooth and slightly tacky. If it is too dry, add a little more lukewarm milk. If it is too sticky to handle, add a little more flour.
5. Grease a large bowl with butter or oil and add the dough, turning to coat. Cover and allow to rest at room temperature until doubled, about 1 hour.
6. On a lightly floured surface, punch down the dough and divide into 3 equal pieces. Form each into a smooth ball, cover, and allow to rest at room temperature for 20 minutes.
7. Grease a loaf pan with butter.
8. On a lightly floured surface, roll one ball into a thin rectangle about 10 x 7 inches (25 x 18 centimeters).
9. Fold the dough lengthwise into thirds.
10. Roll the dough up, short side to short side, sealing the seam, and place in the loaf pan with the spiraled edges facing the long edges of the pan and the seam facing down. Repeat with remaining dough.
11. Cover and allow to rest until the dough puffs up and fills in the pan, about 1 hour.
12. Preheat oven to 375˚F (190˚C).
13. Bake the dough in the preheated oven until golden brown with a solid crust, about 30-40 minutes.
14. Remove from the pan to a wire rack to cool to room temperature before serving.