In a medium saucepan over medium to low heat, place the glutinous rice flour and water. Stir flour and water together until there are no lumps. Stir consistently until the mixture starts to come together. Remove saucepan from heat and continue stirring until a dough like consistency has formed. Set aside to cool. This is the mochi component of the bread.
Grease with butter and line with parchment paper a 24cm (9.4 inches) x 12cm (4.7 inches) x 10cm (3.9 inches) baking tin.
In a stand mixer, place the salt, bread flour, instant dry yeast, brown sugar, butter, egg white, and the mochi dough.
Knead the mixture on low speed until the dough meets the windowpane test. To do this, take a small bit of the dough and stretch the dough into a square. Keep stretching the dough until the middle becomes thin without breaking. If the thin part of the stretched dough is able to pass light through it, the dough is properly kneaded.
Knead for a further 20 minutes on medium speed, or until the dough appears smooth, slightly sticky, and elastic. If the dough seems too dry, add 1 tablespoon of water until it doesn’t look so dry.
Shape the dough into a ball and place the dough in a bowl and cover the bowl in plastic wrap. Put in a warm place to rise until double in size.
Gently punch the dough to release any air from the dough. Then transfer the dough to a lightly floured surface.
Shape and flatten the dough into a 24 cm long rectangle (or as wide as your baking tin).
Place the dough into the prepared baking tin.
Cover the baking tin with plastic wrap and rest for 50 minutes or until the dough has doubled in size.
Preheat the oven to 200°C (392°F).
In a small bowl, combine the egg yolk and milk. Lightly brush the mixture over the bread.
Bake the bread in the oven for 30 to 35 minutesor until golden brown. Lightly spray the oven with water when you put the bread in the oven. If the bread is becoming too brown before it is cooked, place a sheet of aluminium foil on top of the baking tin.
Remove the bread from the oven and allow it to cool slightly in the tin before removing it.