To make the tangzhong, whisk the flour and water until smooth.

Transfer the flour mixture to a small saucepan and warm it over medium heat. As the mixtures heats up, stir continuously. You want to cook the mixture until it thickens and creates "lines" (see the blog post for more details). These lines indicate it's reached approximately 150°F (65°C).  If you are unsure, use a kitchen thermometer to measure the temperature.  Once it's at temperature, turn off the heat and set the pan aside to cool. Once the mixture is cooled transfer it to a bowl and place a piece of plastic wrap large enough to directly cover the surface of the mixture (to protect it from drying out) and to seal the bowl. Place the bowl in the refrigerator and chill it for several hours. You will use half of the tangzhong for this recipe, so keep the leftovers in the refrigerator for up to two days.

In a large bowl, combine the flour, sugar, salt, and yeast. In a separate bowl, whisk one egg, milk, and tangzhong. Make a well in the dry ingredients and pour the wet ones into it. Using your hands, mix the dry ingredients with the wet ones until a loose dough forms and add the butter. Continue mixing until the butter is incorporated. At this point, the dough will be very sticky so remove it from the bowl and knead it on the countertop. Knead the dough until it's no longer sticky. It should be elastic, which means you should be able to stretch a piece of it quite thin without it breaking. This process will take approximately 30 minutes to do by hand. To shorten the kneading process, you can use the kneading function on a breadmaker or a high-powered food processor instead of doing it by hand.

Coat the inside of a large bowl with oil. Shape the dough into a ball, place it in the oiled bowl, and cover the bowl with a wet towel. Leave the dough to proof for 40 minutes or until it has doubled in size.

Transfer the dough to a clean work surface and divide it into four equals parts and shape each into a ball. Cover the dough balls with plastic wrap and rest them for 15 minutes.

Using a rolling pin, roll each dough ball into an oval shape. Fold one end of the dough to the center of the oval. Fold the other end so that it just overlaps the other in the middle. Turn the dough over with the folds facing down and flatten the dough with a rolling pin. Turn the dough over again - with the folds facing up - and, starting at one end, roll the dough up. Repeat with the remaining dough balls. Place each rolled dough in a baking pan. Leave the dough to rise for 40 minutes.

In a small bowl, beat the remaining egg and brush it on the top of the dough rolls in the pan. Bake the bread at 350°F (177°C) for approximately 30 minutes.