Prepare the tangzhong by cooking 2 tablespoons of flour with 1/2 cup water over medium heat until it thickens into a paste. Let cool.
In a mixing bowl, combine bread flour, sugar, salt, and yeast. Add the cooled tangzhong, warm milk, and softened butter. Mix and knead until the dough is smooth and stretchy.
Let the dough rise for 60–90 minutes until doubled in size.
Punch down and shape into a loaf. Place into a greased loaf pan and let rise again for 30–40 minutes.
Bake at 350°F (175°C) for 30–35 minutes. Let cool completely before slicing.
To make tamago sando, boil eggs for 8–9 minutes, cool, peel, and mash with Japanese mayo, sugar, salt, and pepper. Spread between slices of milk bread.
For fruit sando, whip cream with sugar, spread on bread, and layer with sliced fruits. Chill before slicing for clean edges.
To make katsu sando, fry a breaded pork or chicken cutlet until golden, drizzle with tonkatsu sauce, and sandwich between milk bread slices.
Slice sandwiches with a clean, serrated knife. Serve chilled or at room temperature.