Gently punch down the dough and roll it into a 8 x 12 rectangle. Use a little flour to help roll the dough.
Thinly slice the chilled butter into several pieces. Make sure that the slices are thin and not chunky. Also having the butter really cold helps in slicing them neatly.
Place the sliced butter over ⅔rd of the rolled dough. Bring the remaining ⅓ rd of the dough over the butter and then fold the dough over itself one more time, making a tri-fold.
Pinch the edges to seal well, so that the butter does not ooze out when we roll again.
Dust the surface with more flour and roll the dough gently again to form a 8 x 12 rectangle. Try to keep the edges straight.
Now tri-fold the dough again and wrap it plastic and place in the refrigerator for about 30 minutes to chill.
When the dough is chilling, prepare the cinnamon sugar by mixing the cinnamon and sugar in a small bowl.
Also preheat the oven to 400 F. Line a tray with parchment and keep it ready.
When the dough has chilled, remove it from the refrigerator and roll it into a 10 X 15 rectangle.
Brush the surface of the dough with little water and sprinkle the cinnamon sugar evenly.
Start rolling the dough tightly, like a jelly roll and form a tight log. Pinch the edges to seal and with the sealed side facing down, slice the log into 1 inch pieces. I got about 9 pieces from my dough.
Using a rounded wooden stick or the handle of a wooden ladle/spoon, press on the center of each piece strongly and all the way down. You will see the dough flare out and spread on each side like a wing of the bird. This is a step that I really enjoyed as it was very pleasurable to watch the dough spread out.