Reattach the dough hook and turn the mixer on medium-low speed. Add the butter pieces all at once and continue to mix, scraping down the bowl and hook once or twice, until the dough has formed a very smooth, stretchy ball that is not sticky, 8 to 10 minutes.

Form the dough into a ball and place seam-side down on a lightly floured work surface. Using a sharp knife, cut two deep perpendicular slashes in the dough, forming a “+.” (This will help the dough expand into a square shape as it rises, making it easier to roll out later.)

Place the dough slashed-side up inside the same mixing bowl, cover with plastic wrap and let rise at room temperature until about 1½ times its original size, 45 minutes to 1 hour. Transfer the bowl to the refrigerator and chill for at least 4 hours and up to 12. (*My dough is usually perfect at 6.5 hrs, so the schedule here reflects that*)

Remove the dough from the refrigerator, uncover and transfer to a clean work surface. (It will have doubled in size.) Deflate the dough with the heel of your hand. Using the four points that formed where you slashed the dough (as the square corners), stretch the dough outward and flatten into a rough square measuring no more than 8 inches on one side.

Place 2 pieces of plastic wrap on the work surface perpendicular to each other, and place the dough on top. Wrap the dough rectangle, maintaining the squared-off edges, then roll your pin over top as you did for the butter, forcing the dough to fill in the plastic and form an 8-inch square with straight sides and right angles. Freeze for 20 minutes.

Remove the butter from the refrigerator and the dough from the freezer. Set aside the butter.

Unwrap the dough (save the plastic; you’ll use it again) and place on a lightly floured surface. Roll the dough, dusting with flour if necessary, until 16 inches long, maintaining a width of 8 inches (barely wider than the butter block). With a pastry brush, brush off any flour from the surface of the dough and make sure none sticks to the surface.

*Butter and dough should have the same firmness, with the dough slightly cooler. If the butter can't bend without breaking, let sit for a few minutes. Pay special attention to this if you live in a cooler, drier environment.*

Unwrap the top of the butter and use the parchment paper to invert the block in the center of the dough rectangle. Press the butter gently into the dough and peel off the parchment paper. You should have a block of butter with overhanging dough on two opposite sides and a thin border of dough along the other two.

Grasp the dough on one side of the block and bring it over the butter toward the center, then repeat with the other side of the dough, enclosing the butter. You don’t need the dough to overlap, but you want the two sides to meet. Pinch the dough together along all seams so no butter peeks out anywhere. Lift the whole block and dust a bit of flour underneath, then rotate the dough 90 degrees, so the center seam is oriented vertically.

Orient the rolling pin perpendicular to the seam and lightly beat the dough all along the surface to make your butter pliable. Roll out the dough lengthwise (without applying downward pressure, but pushing toward/away from you instead) along the seam into a 24-inch-long, ¼-inch thick narrow slab, lightly dusting underneath and over top with more flour as needed to prevent sticking. Periodically lift the dough and ensure it’s not sticking to the surface, and maintain straight, parallel sides. (It’s OK if the shorter sides round a bit — you’re going to trim them.)

Use a wheel cutter or sharp knife to trim the shorter ends, removing excess dough where the butter doesn’t fully extend and squaring off the corners for a straight-edged, even rectangle of dough. Maintaining the rectangular shape will lead to the most consistent and even lamination. If you see air bubbles in the dough while rolling, pierce them to deflate and proceed.

Form Book: Dust any flour off the dough’s surface. Grasp the short side of the rectangle farther from you and fold it toward the midline of the dough slab, aligning the sides. Press gently so the dough adheres to itself. Repeat with the other side of the dough, leaving an ⅛inch gap where the ends meet in the middle. Now, fold the entire slab in half – this is called a “book” (which is four layers thick).

Wrap the book tightly in the reserved plastic. If it is thicker than about 1½ inches, or if it’s lost some of its rectangularity, roll over the plastic-wrapped dough to flatten it and reshape it. Freeze the book for 15 minutes, then refrigerate for 1 hour.

Let the dough sit at room temperature for about 5 minutes. Unwrap and place on a lightly floured surface. Beat the dough and roll out, as before, into another long, narrow ⅜-inch thick slab. It should be relaxed and extend easily. Dust off any excess flour.

Fold the dough in thirds like a letter, bringing the top third of the slab down and over the center third, then the bottom third up and over. This is a “simple turn,” tripling the layers. Press gently so the layers adhere. Wrap tightly in plastic again and freeze for 15 minutes, then refrigerate for 1 hour.

Meanwhile, line two rimmed baking sheets with parchment paper and set aside. Let the dough sit at room temperature for about 5 minutes. Unwrap (save the plastic for proofing), place on a very lightly floured surface, and, if necessary, re-roll out to 17-by-14 inches. Thoroughly dust off any excess flour with a pastry brush. Use a wheel cutter or long knife and ruler to cut the shorter sides, trimming any irregular edges where not all the layers of dough fully extend and creating a rectangle that’s exactly 16 inches long.

Working one triangle at a time, grasp the two corners of the shorter end, the base of the crescent, and tug gently outward to extend the points and widen the base to about 3 inches. Then, gently tug outward from about halfway down the triangle all the way to the point, to both lengthen the triangle and thin the dough as it narrows.

Starting at the base, roll up the dough, keeping the point centered. Try not to roll tightly or stretch the dough. Place the crescent on one of the parchment-lined baking sheets, resting it on the point of the triangle. If the dough gets too soft while you’re working, cover the triangles and freeze for a few minutes before resuming rolling. Space them evenly on the baking sheets, four per sheet. Very loosely cover the baking sheets with plastic wrap, so the croissants have some room to expand.

Open the oven and stick your hand inside: It should be humid but not hot, as the water in the skillet will have cooled. You want the croissants to proof at 70 to 75 degrees. (Any hotter and the butter will start to melt, leading to a denser croissant.)

Place the baking sheets inside the oven and let the croissants proof until they’re about doubled in size, extremely puffy, and jiggle delicately when the baking sheet is gently shaken, 2 to 2½ hours. Resist the urge to touch or poke the croissants: they’re very delicate. Try not to rush this process either, as an under-proofed croissant will not be as light and ethereal.

*Do not skip this step, as the time to chill will prevent the butter in your croissants from melting out in the oven.*

Remove the baking sheets from the oven and carefully uncover them, then transfer to the refrigerator and chill for 25 minutes while you heat the oven. Remove the skillet from the oven and heat to 375 degrees.

In a small bowl, stir the yolk and heavy cream until streak-free. Using a pastry brush, gently brush the smooth surfaces of each crescent with the yolk and cream mixture, doing your best to avoid the cut sides with exposed layers of dough.

Transfer the sheets to the oven and bake for 20 minutes. Rotate the baking sheets and switch racks, and continue to bake until the croissants are deeply browned, another 10 to 15 minutes. Remove from the oven and let cool completely on the baking sheets.

Whisk on high speed until you reach firm peaks.

Transfer to a piping bag (or a ziploc bag with the corner cut off).