TANGZHONG

1. Make the Tangzhong. Combine the milk and bread flour in a medium saucepan. 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. 

BUNS

1. Add dough ingredients. Add the cold milk and mix to combine, checking with your finger that it is not hotter than lukewarm (the cold milk should cool the hot tangzhong enough). Add the sugar, yeast, milk powder, salt, egg, and flour. Transfer to the mixer and fit with the dough hook. 
2. Mix the dough. Mix the dough on medium speed until it is smooth and elastic and clearing the sides of the bowl, about 12-15 minutes. Don’t freak out, as it is sticky - if you have made it by weight you will be fine. Set a timer and walk away from the mixer if you need. If after that time it really isn’t coming together and you’re worried, add flour a teaspoon at a time just until the dough just comes together. Add the butter and mix for a further 5 minutes until incorporated. The dough should be smooth and elastic, and pass the windowpane test.
3. Rise the dough. Turn the dough out onto a surface and flour very lightly if needed to bring into a tight ball with a bench scraper. Transfer to a greased bowl and cover the bowl with plastic wrap. Place the dough in a warm spot and rise until doubled in size, approximately 1 ½ hours.
4. Divide the dough. Turn the dough out onto a lightly floured surface. Grease and line a 9x13” (23x33cm) baking pan. Divide the dough into 12 equal portions, each weighing about 67g. Working with one piece of dough at a time, flatten out the piece of dough, then tuck up into a ball, then turn the ball seam side down and roll into a tight ball by cupping your hand to create a 'claw' shape, using the tension from the counter to roll the dough tightly. Place to the side and cover lightly with plastic wrap. Repeat with the remaining pieces of dough, grouping the balls together on your counter with a little space between them so they don't touch.
5. Roll the buns. Leave the buns to rest for 10 minutes, then give them a quick roll to tighten them back up. Arrange them evenly in the pan. Alternatively you can space them out individually.
6. Rise the buns. Cover the buns either with a lid, or some lightly greased plastic wrap, or place a second sheet pan upside down over the top to act as a lid. Leave the buns to rise again for about 45 minutes to an hour. You want them to puff up and double in size, and when you press lightly on one, it should leave a small indentation that doesn’t quite spring back. See images for how they look just after rolling and then risen. Remember that rising time depends on your environment so go by how the dough is looking, rather than a rising time.
7. Egg wash and bake. When there is about 20 minutes to go in the rise, preheat the oven to 360°f / 185°c. Brush the buns with egg wash. Bake the buns for 15-20 minutes, until deep golden brown. Remove from the oven. Leave to cool in the pan. The buns will wrinkle slightly as they cool - this is due to them being very soft and is totally normal.

ASSEMBLY

1. Fill the buns. Transfer the jam to a piping bag fitted with a round piping tip or with the tip snipped off. Alternatively you can use a ziploc bag. Poke a hole in the top of each of the buns using a chopstick. Wiggle it around to create space for the jam. Pipe jam into the tops of the buns. If you would like, to check that there is enough jam in the bun so you know how much to add, you can put a clean finger into the bun to check how much jam is in there. (this sounds weird but it's the only way to check haha)
2. Make the icing. Combine all icing ingredients in a medium bowl until a thick, smooth icing forms. Adjust boiling water or powdered sugar until you get the right consistency - you want it to be thick enough to spread. Divide the icing between the buns. Smooth using an offset spatula or the back of a spoon. Leave to set until a slight crust forms on the icing or eat straight away. 

Store leftovers in an airtight container at room temperature.