Whisk 30 g all-purpose flour with 60 ml water in a small saucepan until smooth.

Cook the flour mixture over low heat, whisking constantly, until it becomes a thick smooth paste.

Transfer the tangzhong to a mixing bowl and let it cool until lukewarm.

Whisk 100 ml milk, 6 g active dry yeast, and about 1 teaspoon of the caster sugar in a mixing bowl.

Set the yeast mixture aside for about 5 to 10 minutes until foamy.

Add the remaining all-purpose flour, remaining caster sugar, cooled tangzhong, eggs, and yeast mixture to the stand mixer bowl.

Knead the dough with the stand mixer until smooth and elastic, about 8 to 10 minutes.

Add 50 g softened unsalted butter gradually while the mixer runs.

Continue kneading until the dough passes the windowpane test and stretches thinly without tearing.

Place the dough in a lightly buttered mixing bowl and cover it.

Let the dough proof in a warm place until doubled in size, about 60 to 90 minutes.

Punch down the risen dough and divide it into 3 equal portions.

Shape each dough portion into a tight roll or folded loaf shape.

Place the 3 shaped dough portions seam-side down in the 9 x 5 inch loaf pan.

Cover the loaf pan and proof the dough until doubled and puffy, about 45 to 60 minutes.

Preheat the oven to 210°C (410°F).

Brush the risen dough evenly with egg wash.

Bake the loaf at 210°C (410°F) until golden brown, about 15 to 20 minutes.

Remove the bread from the pan and place it on a wire rack.

Brush the hot bread with 14 g butter for brushing, then let it cool before slicing.