Please note that I have included two methods below for tangzhong making and dough kneading using either (A) conventional bread machine or (B) Thermomix so do take note of the sub-headings.

(A) CONVENTIONAL – Tangzhong & Dough Kneading

• Prepare tangzhong by mixing flour in water and whisk together in a pot, ensuring the mixture is well combined with no lumps. Cook over medium-low heat, stirring consistently to prevent burning and sticking while you cook.
• The mixture will gradually become thicker. Once you notice that some “lines” appear in the mixture for when you stir with the spoon, it’s done. Your tangzhong is ready.
  
• Transfer into a clean bowl. Cover with a cling wrap sticking onto the surface of tangzhong to prevent it from drying up. Let cool for 15-20 minutes. You can pre-make the tangzhong ahead of time and store it chilled in the fridge for a few days. If you've chilled your tangzhong, ensure to return it at room temperature first before using.
• Whilst tangzhong is cooling, in a small bowl, add 1 tbsp of milk and sift matcha powder into the milk. Stir to combine and dissolve matcha powder completely. Set aside.
• When tangzhong has cooled completely, add all ingredients (except butter) into breadmaker; first the wet ingredients (egg, milk, tangzhong), then followed by the dry ingredients (sugar, salt, flour, milk powder, yeast).
• If using breadmaker, select "dough" mode and let knead until all ingredients come together, usually I let it knead for approximately 8-9 minutes. If using stand mixer, use dough hook to knead until ingredients come together.
• Then add in the butter, continue kneading until the dough is smooth and elastic. The time of kneading in the breadmaker should take approximately 20-25 minutes. For those using stand mixer, upon 20 minutes of total knead time, check to see if dough has achieved windowpane stage.
• Remove dough and transfer to pastry mat. Divide dough into two equal portions. Leave one to rise, and place the other back into mixing bowl. Add matcha mixture from (4) into mixing bowl and knead for 3-4 minutes until well incorporated.

(B) THERMOMIX – Tangzhong & Dough Kneading

• To make the tangzhong, place 20g high protein flour and 100g milk in mixing bowl, cook for 3min/80°C/spd 3 and let stand for 10-15 minutes until temperature lowers down to 37°C.
• Whilst tangzhong is cooling, in a small bowl, add 1 tbsp of milk and sift matcha powder into the milk. Stir to combine and dissolve matcha powder completely. Set aside.
• Add 130g milk, egg yolk, sugar, salt, milk powder, remaining 280g high protein flour and yeast then knead 4min.
• Add butter, knead 1min.
• Remove dough and transfer to pastry mat. Divide dough into two equal portions. Leave one to rise, and place the other back into mixing bowl. Add prepared matcha mixture into mixing bowl into and knead 30 seconds until well incorporated.

Bulk Fermentation & Dough Shaping

• Transfer matcha dough to pastry mat and shape both doughs into smooth, round balls. Let proof in a warm place covered loosely with clingwrap/damp towel until doubled in size (approx. 45-60 minutes). 
• Grease hands lightly with neutral flavoured oil or butter, then punch down both milk and charcoal dough to deflate. Divide milk dough into 6 equal portions. To pre-shape, roll each portion into a round, even ball then let sit on bench to rest, covered for 15 minutes.
  
• Shape each portion into tight round balls and place in a greased 450g loaf pan alternately. This means if you are placing a milk dough on the bottom, you will need to place a matcha dough next to it on both sides, and also above it as per example below:
  
• Let dough rise for its 2nd round of proofing, until double in size. This takes another 35-40 minutes depending on the weather. The best temperature for 2nd round proofing is 38°C, humidity 85%.

  Note: If you are not in a tropical climate or if it is winter where you are, place a cup of hot water inside the oven, set to 35-38°C and allow your dough to rise inside. Alternatively, you may also heat up a cup of water in the microwave for 60 seconds then proceed to cover dough with a cloth/cling wrap, and let rise inside the microwave. 
  
• During last 15 minutes, preheat oven to 190°C.
• As we want to achieve a nicely square-shaped loaf, put on greased lid and bake at 190°C for 25 minutes, then lower down the temperature to 180°C and bake for a further 10 minutes.
• Remove bread from tin and allow to cool completely on a cooling rack for at least an hour before slicing and serving.