Remove one piece of the chilled dough from the refrigerator. While the dough is still in the plastic wrap, firmly but gently tap on it with the rolling pin until it is flexible but still cold. Lightly dust the work surface with flour. Place the disk of unwrapped dough on the surface and lightly flour the top of the disk with flour.
Place the dough on a sheet of parchment paper and, using a rolling pin, start rolling the dough from the center to the edge, away from you. Do not use too much pressure, or the dough will crack. Roll it into a 13 by 13-inch square, reflouring the top of the dough to prevent the dough from sticking as necessary.
Using a pastry wheel and a ruler as a straight edge, cut the dough into approximately 1/3-inch strips.
Slide the parchment onto a baking sheet and place it in the fridge to chill while proceeding with the following steps.
Repeat steps 1-3 with the second disk of dough. If your baking environment is warm and the dough feels soft, slide the sheet of parchment onto a flat baking sheet and chill the dough in the fridge for 5 minutes. If your dough gets warm at any point in the weaving process, you can slide the sheets of parchment on a flat baking sheet to chill the dough in the fridge for several minutes.
Place one set of dough strips on parchment on your work surface so the strips are oriented vertically. Starting from the left side, fold back the first four strips of dough halfway. Skip the next four strips and then fold back the following four. Continue in this pattern until you run out of strips. Retrieve a dough strip from the second sheet of parchment and place it horizontally. This strip should lay across the center of the whole square. Unfold all the vertical strips.
Starting again from the left side, leave the first strip. Fold the next three strips back. Leave the next three strips and fold back the following single strip. Leave a strip and begin the pattern again until you reach the right side. Retrieve a dough strip from the second sheet of parchment, place it horizontally, and unfold all the vertical strips.
Starting from the left side, leave the first two strips. Fold back the next two strips. Leave the next two and fold back the following two. Continue in this alternating pattern until you reach the right side. Retrieve a dough strip from the second sheet of parchment, place it horizontally, and unfold all the vertical strips.
Starting from the left side, leave the first three strips. Fold back the next single strip. Leave the following single strip and then fold back the next three. Continue in this pattern until you reach the right side. Retrieve a dough strip from the second sheet of parchment, place it horizontally, and unfold all the vertical strips.
Starting from the left side, leave the first four strips and fold back the following four. Continue in this alternating pattern until you reach the right side. Retrieve a dough strip from the second sheet of parchment, place it horizontally, and unfold all the vertical strips.
Starting from the left side, fold back the first strip. Leave the next three strips, and then fold back the next three. Leave the following strip and then repeat the pattern. Retrieve a dough strip from the second sheet of parchment, place it horizontally, and unfold all the vertical strips.
Starting from the left side, fold back the first two strips. Leave the next two and then fold back the following two strips. Continue this pattern. Retrieve a dough strip from the second sheet of parchment, place it horizontally, and unfold all the vertical strips.
Starting from the left side, fold back the first three strips. Leave the next single strip and then fold back the following single strip. Leave the next three strips and then repeat the pattern. Retrieve a dough strip from the second sheet of parchment, place it horizontally, and unfold all the vertical strips.
Repeat steps 6-13 until you reach the end of the vertical strips.
Rotate the sheet of parchment containing the woven dough 180 degrees. The unwoven strips should be oriented on the bottom half of the square.
Repeat steps 7-13 in descending order to complete the full sheet of woven dough.
Slide the sheet of parchment on a flat baking sheet and place it in the freezer for 10-15 minutes or until the woven dough is frozen solid.