In a mixer with a dough hook, place the yeast, flour, sugar, salt and the milk and mix for 2 minutes until a soft moist dough forms on the hook. If most of the flour isn't moistened with this quantity of milk, add more, a tablespoon at a time until it is moistened and smooth, using up to 4 tablespoons. Turn mixer on high and mix for another 4 minutes until very smooth and elastic.
Turn the dough out of the bowl onto a floured board, cover with a damp tea towel and allow it to rest for 15 minutes to relax the gluten. Remove the towel and, using a French rolling pin, roll the dough into a 10 by 9-inch rectangle 5/8-inch thick. Wrap in plastic then chill for 1 hour and up to overnight.
Ten minutes before the dough is done resting in the refrigerator, prepare the butter. Beat it with your rolling pin on a floured surface to soften it and form a rectangle 6 by 8 ½ inches. Place it between parchment paper or plastic wrap and set aside.
Remove the dough from the refrigerator and roll it on a floured work surface into a 10 by 15-inch and ¼ inch thick rectangle. Brush any excess flour off the dough. Place the shorter side of the dough parallel to the front of your body on the work surface. Place the butter in the middle, long-ways. Fold the bottom up over the butter and brush off any excess flour and then fold the top down over the butter to overlap and encase the butter. Press down lightly with the rolling pin to push all the layers together and make sure they have contact.
Continue rolling the laminated (layered) dough to form a new 10 by 15-inch rectangle, patching any holes with a dusting of flour where butter may have popped through. Fold into thirds, like a letter, brush off any excess flour and mark it with an indentation made by poking your finger once at the corner of the dough meaning you have completed the first "turn".
Wrap well in plastic and chill 1 hour and up to overnight. Do this again three more times (some people only do 3 turns total, some do 6, some do 3 plus what's called a "wallet" turn for the last one which is a 4 fold turn that's folded into itself like a book jacket) marking it accordingly each time and chilling in between each turn.
After the fourth turn, you can let the dough chill overnight, or, for 1 hour, or, roll it out to a 13 by 24-inch square that is a little less than ¼-inch thick and cut out your croissants and shape them.
It is easier to roll out the dough and cut it with a sharp large knife into 6-inch strips then cut them into triangles, 4 inches wide at the base of the triangle (or for a more curved croissant cut the triangles 6 inches wide). Stretch these triangles again 9 inches long, then place on the work surface and put a piece of scrap dough in the center of the wide end to enclose, which will plump up the center. Roll the triangles up towards you starting at the wide end and place them 2 inches apart on a parchment lined sheet pan with the tip tucked under and the ends slightly curved in to make a crescent shape. You may freeze the croissants at this point, or, in a small bowl, whisk together the egg and milk and brush the croissants with this egg wash.
To proof the croissants, place them in an oven that is warm but not turned on, with a pan of hot water in the bottom to create a moist environment like a proof box. Set aside to proof for 1 ½ to 2 ½ hours until puffed up and spongy to the touch. Remove from the oven.
Spritz a preheated 425 degree F oven with water, close the door, and get the croissants. Place the croissants in the oven and spritz again, close the door and turn the oven down to 400 degrees F. After 10 minutes, rotate your pan if they are cooking unevenly and turn the oven down to 375 degrees F. Bake another 5 to 8 minutes until golden brown.