Combine dry ingredients - Add the bread flour, salt, sugar and instant dry yeast to the bowl of a stand mixer fitted with a dough hook. Mix until well combined, about 20 seconds.
Add wet ingredients - Add the Tangzhong, milk and egg and mix until a dough forms. Then add all of the softened butter and mix until everything is combined. Continue mixing for 10 minutes on low speed. The dough will be very smooth.
First rise - Cover with plastic wrap or a lid and allow to rest in a warm spot for 1-2 hours or until it’s doubled in size.
Prepare baking tin - Line a 9x13-inch/23x33cm baking tin with baking paper. Brushing it with a little melted butter will help the baking paper stick.
Weigh out buns - Dust your workbench with flour and pour the risen dough onto the bench. Knead a little to form a large ball. Divide the dough into 12 even sized portions by weighing them using a kitchen scale. Each portion should weigh the same. This will ensure even sized buns.
To form dough balls - Place a cupped hand over one dough piece and swirl around on the bench top until it forms a ball. The slight stickiness of the dough will grip onto the work bench and help shape it under your hand forming a tight ball. Place the dough piece in your baking tin with the smooth side up. Repeat this until you’ve shaped all your buns.
Second rise - Cover loosely with plastic wrap that’s been lightly oiled (so it doesn’t stick to your buns) and let them rise for 1 hour.
Bake - 15 minutes before you’re ready to bake, preheat a fan forced oven to 180C/355F (200C/400F for no fan). Once the buns are risen, brush lightly with egg wash (egg and water whisked together) Bake in the middle rack of your oven for 20-25 minutes or until golden brown. Serve warm or cooled to room temperature. These rolls stay soft for days, especially when served at room temperature.