First, prepare the Tang-Zhong. In a small saucepan, pour the 120g of milk and 25g of bread flour. Place over medium heat and cook, stirring continuously, until the mixture thickens into a paste. Remove from heat and transfer to the bowl of a stand mixer and set aside for a few minutes to cool.
In a bowl, add the rest of the milk, caster sugar, dried yeast and mix to combine, set aside for 5 minutes to activate the yeast.
Then, add the flour, salt and add the yeasted milk mixture and the egg to the mixing bowl with the Tangzhong. Mix with the dough hook on medium speed until it is smooth, elastic and sticky but clearing the sides of the bowl, about 12-15 minutes.
Add the cubed butter and mix for a further 5 minutes until fully incorporated. The dough should be smooth and elastic. Remove from the mixing machine. Scrap the edges to ensure the butter is fully combine and cover the bowl with cling film.
Place the dough in a warm area and rise until doubled in size, approximately 1 ½ hours.
Turn the dough out onto a lightly floured surface.
Divide the dough into 90g balls (About 9 balls or more if you prefer smaller burger bun). Roll the ball with your hand into a smooth bun. Place on a baking tray giving spaces for each roll to proof. Cover loosely with a layer a oiled cling film. Leave the buns to rest and proof for about 60-90 minutes. They will double in size, and when press lightly on one, it should leave a small indentation that doesn’t quite spring back.
Preheat the oven to 180˚C. Brush the buns with egg wash and sprinkle with sesame seeds if desired.
Bake in the oven for 15-18 minutes, until they are golden brown. Remove from the oven. Set aside to cool on a wire rack for 10 -15 minutes.
The buns will wrinkle slightly as they cool. Store the buns in an airtight container at room temperature. They should stay soft for at least 5 days or can be frozen. Use the bun as required.