- 1.
**Make the Milk Bread Dough:** In a large bowl, combine bread flour, sugar, salt, and instant dry yeast. Mix well.
- 2.
In a separate bowl, whisk together lukewarm milk, heavy cream, and egg. Pour the wet ingredients into the dry ingredients and mix until a shaggy dough forms.
- 3.
Add the softened butter to the dough and knead until smooth and elastic. This can be done by hand (about 10-15 minutes) or with a stand mixer (about 8-10 minutes).
- 4.
Cover the dough with plastic wrap and let it rise in a warm place for about 1-1.5 hours, or until doubled in size.
- 5.
**Shape and Bake the Bread:** Preheat oven to 350°F (175°C).
- 6.
Punch down the risen dough and divide it into four equal portions.
- 7.
Roll each portion into an oval shape, then fold it in half lengthwise. Roll it up tightly from one end to the other.
- 8.
Place the rolls in a greased 9x5 inch loaf pan, seam-side down. Cover with plastic wrap and let rise for another 30-45 minutes, or until almost doubled in size.
- 9.
Bake for 30-35 minutes, or until golden brown on top. If the top starts to brown too quickly, cover it loosely with foil.
- 10.
Let the bread cool completely in the pan before slicing.
- 11.
**Make the Egg Salad:** Place the eggs in a saucepan and cover with cold water. Bring to a boil, then remove from heat and let sit for 10 minutes. Cool eggs in ice water, peel, and dry.
- 12.
Roughly chop the hard-boiled eggs and place them in a mixing bowl.
- 13.
Add the Japanese mayonnaise, milk, sugar, salt, pepper, and mustard (if using) to the eggs. Gently mix until combined. Be careful not to overmix, you want the eggs to remain slightly chunky.
- 14.
**Assemble the Sandwich:** Cut thick slices of the cooled milk bread. Spread a generous amount of egg salad on one slice of bread, and top with another slice.
- 15.
Gently press the sandwich together. You can trim the crusts if desired.
- 16.
Cut the sandwich in half and serve immediately or chill for later.