For the roux, add the flour and water to a mixing bowl. Whisk until smooth.
Transfer the mixture to a pan and stir well.
Cook until the temperature reaches 150 degrees.
Cover the mixture and chill for a few hours.
For the milk bread, combine the flour, yeast, sugar, and salt in another bowl.
Combine the milk, the roux, and one egg in another bowl. Mix well.
Create a hole in the middle of the dry batter, and pour the wet mixture into it.
Mix with your hands until smooth. Add the butter.
Stretch the dough until it is no longer sticky.
Shape the dough to give it a ball-sized form and transfer it to a bowl. Cover and let it rise.
Place the dough on your work surface and cut it into equal parts. Shape each part into a ball.
Cover the balls and let them rest for between 30-45 minutes.
Roll each dough into an oval size.
Let the pieces rise again, which should take an hour.
Place the dough into a baking sheet.
Beat the other egg and brush it on top of your dough pieces.
Bake in the oven at 350 degrees for 30 minutes.