Make and Laminate the Dough:

1. For the croissant dough: In the bowl of a stand mixer fitted with a dough hook, add all of the dough ingredients in this order: water, milk, instant yeast, sugar, bread flour, salt, and softened butter cubes.
2. Turn the mixer on low and mix until the dough comes together and the sides of the bowl are clean. Continue kneading the dough in the machine for 5 minutes.
3. Transfer the dough to a work surface and knead for 1 minute to ensure the butter is fully incorporated. It's okay if the dough is not smooth.
4. Place the dough in a covered bowl or container and let rise for 1-2 hours, until the dough is just about doubled in size. Do not let the dough proof beyond doubling in size.
5. When doubled, remove the dough from the container and flatten it to remove any gas bubbles. Wrap the dough in plastic wrap and transfer it to the freezer while the croissant butter is prepared. It should be there for no more than 15 minutes.
6. For the croissant butter: Add the softened butter to a clean stand mixer bowl and sprinkle the flour on top. Using the paddle attachment, mix on low until the butter and flour are combined. Scrape the butter off the paddle and mix again for about 30 seconds to ensure the butter is smooth with no unmixed butter or flour. 
7. Remove the croissant dough from the freezer. Roll the dough to a rough 10-by-20-inch rectangle on a lightly floured work surface. Brush off any excess flour using a dry pastry brush.
8. Using an offset spatula, spread the butter on the bottom 3/4 of the dough, going all the way to the edges. There should be no butter on the top ¼ of the dough.
9. Take the top of the dough and fold it down about 1/4 of the way down (about 5 inches). Repeat this fold twice more (taking the top part of the dough and folding it ¼ of the way down) until the butter is no longer visible.
10. Rotate the dough counterclockwise 90 degrees so the dough seam faces the right.
11. Evenly roll out the dough lengthwise, using flour as necessary, to a rough 8-by-20-inch rectangle. Brush off any excess flour.
12. Take the top short side of the dough rectangle and fold it ⅓ of the way down. Repeat with the bottom short side up, like a business letter.
13. Wrap the dough tightly in plastic wrap, then refrigerate for 2 hours.
14. Pre-shape the dough: Evenly roll out the chilled dough to an 8-by-12-inch rectangle, or as close as possible to this. Do not fight the dough. If it’s springing back, leave it as is, wrap it in plastic, and place on a sheet pan. Chill the dough for 15-30 minutes.
15. Using only a very light dusting of flour, if any, roll out the chilled croissant dough to the final length of 10 by 16 inches.
16. Using a ruler and a pastry wheel, cut off any uneven edges of the rectangle, especially on the left and bottom sides.
17. Cut 7 isosceles triangles in the dough. To do this, premark the dough with 3 very small notches, 4 inches apart on the bottom. Then, starting 2 inches in on the top, premark 4 notches 4 inches apart. Connect those notches from bottom to top, then top to bottom, resulting in 7 perfectly cut isosceles triangles. Two half triangles will remain; connect those together to complete 8 triangles.

Shape and Bake the Croissants:

1. Working one piece at a time, take hold of the base of the triangle and gently elongate it by placing your other hand towards the middle of the triangle and pulling the dough, letting it glide through your hand as it stretches. It should gently elongate the tip of the triangle, but be careful not to squish the layers. Then grasp the two corners of the base of the triangle and tug gently outward to extend the points and widen the base. 
2. Roll up the dough starting at the base, keeping the tip of the triangle centered. Do not roll too tightly. Give a gentle push down on the rolled-up crescent to secure the tip of the dough on the bottom.
3. Repeat this process with the remaining triangles of dough.
4. Place four croissants each on two parchment-lined sheet pans. Very loosely cover the baking sheets with plastic wrap to prevent the dough from drying out.
5. Let proof in a warm place for 2-4 hours, or until the croissants have nearly doubled in size and are incredibly jiggly.
6. Place a rack in the lower middle and the middle parts of the oven and preheat the oven to 425ºF.
7. When the oven is ready, carefully remove the plastic wrap from the croissants. Brush the smooth tops of the proofed croissants (not the exposed cut edges) with the egg wash. Using a clean, food-safe spray bottle, spritz cold water on the parchment around the croissants to create steam in the oven (which helps the croissants bake up taller).
8. Turn the heat down to 375ºF and bake the croissants in the oven for 24-26 minutes, switching and rotating the trays halfway through, or until the croissants are a beautiful golden brown.
9. Remove the croissants from the oven, and let cool briefly before enjoying.
10. Croissants are best enjoyed fresh. To store, let sit at room temperature for 24 hours, and beyond that in a covered container. Croissants can be “refreshed” in the toaster oven