Flour a large cutting board or your countertop, and roll out puff pastry dough to 12 x 9.5 inches.
Turn the dough so the wider side is horizontal. Then cut in half in the middle of the long side to make two tall rectangles, each 6 x 9.5 inches.
Combine sugar and cinnamon in a small bowl.
Spread softened butter over each puff pastry rectangle, leaving a ½ inch border on the top (wide) side.
Sprinkle cinnamon-sugar mixture evenly over the butter.
Whisk egg in a small bowl. Use a pastry brush to paint the border of the puff pastry sheet that you left clear.
Then, starting from the other end, roll up lengthwise as tightly and gently as possible. Press gently but firmly along the edge with the egg wash to seal.
Place on a cutting board or plate and put in the freezer for 30 minutes.
While the puff pastry roll is in the freezer, preheat oven to 400 degrees Fahrenheit. Line two baking sheets with parchment paper.
Remove rolls from the freezer when they are firm, and slice into ⅓-inch slices.
Arrange onto sheet pans leaving at least an inch of space around each pinwheel.
Bake for 15 minutes, until lightly browned on both top and bottom. Let cool slightly before serving.
Notes
Make-Ahead Notes: You can make these Cinnamon Swirls well in advance, since they need chilling time in the freezer anyway. To freeze for longer than the 30-minute chill time, wrap the cylinders in parchment paper and twist each edge to seal. Store in the freezer for up to two months. Defrost in the refrigerator before slicing and baking (do not defrost at room temperature since you need the cylinders to be quite cold to slice cleanly). Puff Pastry Tips: The key to these Cinnamon Swirls is working with your puff pastry dough at the right temperature. If your dough came in a sheet that is folded in thirds, make sure you wait until the dough is defrosted (but not too soft) to unfold it. Unfolding the dough when it is still quite cold can cause it to break or tear. Then, don’t wait too long to begin working with your defrosted dough. If it is out too long at room temperature and becomes too soft to work with, just put your dough into the refrigerator at any time to firm it back up. For example, if it is too difficult to roll up your dough with the filling in it because the dough is too soft, just place the unrolled pinwheels into the refrigerator (or freezer) for a few minutes. (This is where it is useful if you rolled your dough out on a cutting board rather than the counter!)