Preheat oven to 400 degrees. Line a cupcake/muffin pan with 8 liners and set aside. Or, line a 10 inch round baking pan with parchment paper and set aside.
Roll thawed puff pastry sheet out with a rolling pin to about a 12 inch square. Using a pastry brush, brush melted butter over the entire surface.
In a small bowl, mix together the brown sugar and ground cinnamon. Sprinkle sugar mixture evenly over dough.
Starting at one end, roll dough into a log. Slice log into 8 even pieces and place each into a muffin liner (or about 1 inch apart into round baking pan).
Bake for 20-22 minutes, or until tops are lightly browned. Remove from oven.
In a bowl, combine confectioner's sugar, milk, and vanilla. Stir until mixture is fully combined. If too thick, add more milk ½ tablespoon at a time.
Drizzle over warm cinnamon rolls and serve immediately.
Baking in muffin pan liners ensures your cinnamon rolls all bake evenly, and reduces messy cleanup after breakfast. I do not recommend baking cinnamon rolls without paper liners, because they are delicate and hard to remove straight from the pan.
If you don't have a muffin pan, line a 10 inch baking pan with parchment paper and place your cinnamon rolls about 1 inch apart. I do not recommend baking on a baking sheet, because they will unravel if given too much space to bake.
For added crunch, add ¼ cup of chopped pecans or walnuts with your cinnamon/sugar mixture.