In a medium-sized bowl, combine the warm milk, sugar, and yeast. Allow to bloom for 5 to 10 minutes until frothy.
In the bowl of a stand mixer, combine the bread flour and salt.
Add the yeast mixture and beaten eggs to the flour and salt. Knead on low speed for 3 to 5 minutes until a shaggy dough forms, scraping down the sides of the bowl as needed.
Add the cold, cubed butter and knead for an additional 8-10 minutes until the butter is fully incorporated and the dough is smooth.
Turn the dough out onto a lightly floured surface, and form it into a tight ball. Place in a lightly greased large bowl, turning to coat. Cover and let rest for 1 hour, or until doubled in size.
Punch the dough down and divide into six equal pieces. Roll each into a rectangle about 9 inches wide by 5 inches tall.
Starting with the long side, roll the dough tightly into a loaf shape and pinch the seams together. Place seam side down on a baking sheet lined with parchment paper.
Cover with a damp cloth and let rise for 30 minutes. Meanwhile, preheat the oven to 400°F.
Mix the egg white and water. Brush this mixture over the loaves and score the dough ¼ inch deep in three spots.
Bake for 15-20 minutes until golden brown or until they register 195-200°F internally.