Preheat your oven to 400°F (200°C).
Lay a thawed, but still cold sheet of puff pastry on a lightly flour dusted surface or a piece of parchment.
Roll the dough slightly to blend the creases in and even it out.
Spread the butter all over the dough.
Add the brown sugar on top of the buttered puff pastry, leaving the outer edge empty.
Gently press the brown sugar down into the dough.
Add the cinnamon evenly over the top.
Tightly roll the dough, working in the same direction as the creases of the dough.
Press the seam into the roll gently to help seal it.
If using an egg wash, whisk the egg well and then brush it along the seam.
Brush the tops of the cinnamon rolls with the egg wash.
Lay the roll seam down, and use a sharp serrated knife or dental floss to cut into about 1 ½ inch rolls.
Place on a cookie sheet lined with parchment.
Bake for about 20 minutes or until golden brown and puffed.
Remove from the oven and allow to cool for about 10 minutes.
While cooling, whisk together the icing ingredients, adding only 2 tablespoons of milk to start and more as desired.
Ice the cinnamon rolls and serve immediately.
Store any leftovers in an airtight container.