In the bowl of a stand mixer, whisk together bread flour, sugar, salt and yeast. Once mixed, add in milk and start mixing with the dough hook attachment. Add the water little by little.
Beat for about 5 minutes on a low speed. The dough will be very sticky at first but keep kneading. After 5 minutes and once it comes together, add the butter and beat for about 1 minutes on a low speed. Once the butter is incorporated, beat for another 7-10 min on a medium speed.
Check the consistency (I show how the dough should look in the video, so please check it), and if it's ok, transfer the dough to a lightly floured surface and shape the dough into a ball. Place into a bowl and cover with plastic wrap. Keep the bowl in a warm place(30℃/86℉) for 1 hour or until the dough has doubled in size.
Transfer dough onto a lightly floured surface and press the dough with your palm to remove the gas bubbles formed by the yeast. Shape the dough into a ball and put it back to the bowl, cover with plastic wrap and let sit for another 30 min in the warm place.(30℃/85℉)
Transfer the dough onto a lightly floured surface and divide into 2 equally sized pieces. Shape into a ball and place onto a plate cover with a damp cloth. cover with plastic wrap and let sit for another 30 min in the warm place.(30℃/85℉)
Roll each out and then fold each of the long sides. Starting on one of the shorter edges, roll up the dough a little tightly. Place it into a greased loaf pan, and repeat with the other dough.
Cover the loaf pan with plastic wrap and let the dough proof in a warm place(38℃/100℉) for 45 min or until the dough rises to just below the top of the loaf pan.
Preheat oven to 200℃/400℉. Once the dough has risen, brush the top of the dough with egg. Bake at 200℃/400℉ for about 30 min. If the surface starts to get golden color on top too much in the oven, place a piece of foil over the surface to prevent it from burning.
Once take the loaf pan from the oven, drop it immediately and remove the bread from the pan. Let it cool on a wire rack.