Put 20 gr flour in a saucepan. Mix in 50 ml water and 50 ml milk gradually using a whisk.
Cook the mixture on a low setting until it thickens, mixing all the time.
Set aside and let it cool.
If you are using a stand mixer: Place the bread flour, milk powder, sugar and yeast in the bowl and mix a little. Add the water and eggs and all of the Tangzhong starter. Knead on the lowest speed for 5 minutes. Add the butter little by little. Mix on a medium speed until the dough comes away from the sides and dough temperature measures between 24° and 26°C (75 to 78°F). This can take a good 10 minutes.
If you are mixing by hand. Place the bread flour, milk power, sugar and yeast in the bowl. Rub in the butter. Add the Tangzhong starter. Add the salt and mix. Add the water and eggs. Knead until very smooth (about 10 minutes). It should be smooth and supple and measure between 24° and 26°C (75 to 78°F)
Cover and allow to prove for about 1 hour. It should be well rise and if prodded with a finger the hole should refill slowly.
Cut into four equal pieces. Roll into balls and leave for 10 minutes.
Roll out each piece to about 20 cm by 16 cm.
Fold the top third towards the centre. Fold up the bottom third to the centre. Turn 90 degrees and roll the thinner edge up very tightly.
Place all four rolls next to each other in the bread tin. Brush with beaten egg. Allow to prove for 45 minutes to an hour. The bread will be will risen.
Pre-heat your oven to 180°C/350°F 30 minutes before the bread is ready to bake.
Brush with egg a second time and bake for about 30 minutes until a dark gold. Test to see whether it is done as you would a cake. Insert a knife into the centre, it should come out clean. Allow to cool in tin. It does colour quickly so cover with baking parchment if necessary.
You can of course use this mixture to make rolls. Divide the dough into 90 gr pieces. Shape into balls. Then allow to prove as above. The rolls will need about 15 minutes to bake.