In a small bowl, with your fingers or a fork, mix together the brown sugar and cinnamon.
⅔ cup brown sugar, 4 teaspoons ground cinnamon
Dust a clean work surface with flour. Remove one of the dough squares from the fridge and place it on the flour. Dust the top with flour and roll into a rectangle about 12 inches wide x 10 inches deep. If any of the edges crack, pinch them back together.
Brush the top of the dough with half of the butter, leaving about a ½ inch strip at the top (farthest part from you) unbuttered. Quickly sprinkle the brown sugar mixture on top of the butter, not the strip left unbuttered. Lightly press down on the brown sugar cinnamon mixture onto the dough to make it stick.
6 tablespoons salted butter
Using a pastry brush or simply with your fingers, get the edge with no sugar or butter on it slightly damp with water. This will help the roll stick together and keep the cookies from opening up when baked.
Starting on the side closest to you, roll the dough tightly (a 12-inch side) toward the side that has no butter or sugar mixture on it. Make sure the edge is sealed nicely.
Use a knife or dental floss to cut the roll into about 20 pieces (about ½ inch thick cookies).
Place on the prepared baking sheets. 12 can fit on one sheet. Put the remaining cut cookies in the fridge while the first bake, before baking the second sheet.
Bake for about 10-12 minutes till nearly set. Let the cookies cool on the pan for 8-10 minutes before transferring to a cooling rack to finish cooling.
Repeat the process with the remaining dough in the fridge till all the cookies are baked.