Fold a piece of parchment paper into a 10 inch square, set aside.
Temper butter for the beurrage by hitting it with a rolling pin then placing it in the bowl of the stand mixer fitted with the paddle attachment and add in flour. Mix on low until no visible butter remains.
Place inside parchment paper square, spreading the butter a bit with the back of a bowl scraper, then closing the parchment square back up. Flip it over so the seams are toward the table. Roll out in parchment to a 10 inch square. Refrigerate 30 minutes. I like to do the beurrage first because then I don’t need to clean my bowl before I move on to the next step.
Combine dry ingredients for the détrempe in the bowl of a stand mixer fitted with the paddle attachment. Add the softened butter and cut in butter until no visible butter remains. Combine water and vinegar.With the mixer on low, pour in the water/vinegar mixture into the flour. Mix until a dough forms. Turn dough out onto unfloored surface and gently knead until no dry bits remain (dip your hand in cold water and moisten specific areas if needed).
Press or roll into a 6.5 inch square and wrap in plastic wrap and chill 30 minutes.
Remove the butter from the refrigerator 5-7minutes before the dough. Generously flour a smooth surface and remove beurrage from the parchment onto floured surface.
Placing the dough packet on top of the beurrage so that the dough looks like a diamond on top of the butter. It will be easier to fold the corners of the butter over the dough if they are offset.
Enclose the détrempe inside the beurrage and seal the seems by smooshing the butter together, working quickly so that the butter does not melt.
Roll out until ¼ inch thick and is 18 inches long by 7 inches wide. Perform an envelope fold by folding the dough like you woulda piece of paper to go inside and envelope. Fold the top third down and then overlapping with the bottom third. Repeat once more before wrapping in plastic wrap and chilling for 30 minutes.
Repeat two more sets of two single turns making sure to chill 30 minutes between each set. During the final set the dough will have developed more gluten and will be more resistant to rolling. If the dough begins to shrink, then place it flat on a baking sheet covered with parchment and refrigerate 10 minutes.
After you complete all six single turns, wrap in plastic wrap and chill 2 hours or overnight. Overnight is best!
Roll 1/8 inch thick, chilling as needed to prevent the dough from getting too warm or shrinking. I find it easier to roll it about the sizeof a baking sheet, chill and then slice the dough in half with a pizza cutter.Continue rolling one half while the other half chills and then swap them out as they warm up or start to shrink until they are both about 1/8 inch thick. You will end up with two pieces of dough the size of a baking sheet.
Before using the dough be sure to chill it at least 30minutes. Cut into the desired shape, dock the dough and then chill it once more before baking. Do not allow the dough to temp before baking or you will not get those nice layers.
Bake in an oven preheated to 375°F (preferably convection) according to recipe instructions.