Line a sheet pan with parchment paper and preheat the oven to 400F degrees.
Next, combine the cinnamon and sugar in a small bowl and set aside.
Place the sheet of puff pastry on a lightly floured work surface. Using a rolling pin, roll out the dough lightly to flatten the seams and make an even square. Don't roll the dough out much thinner than it already is.
Brush the pastry with melted butter and sprinkle the surface evenly with the cinnamon sugar, leaving a 1/4" border on all sides.
Starting at the bottom edge closest to you, gently roll the dough up into a tight log. The seam side should be underneath the log.
Using a sharp knife or a bench scraper, trim off the uneven ends and cut the log into eight equal pieces.
Arrange the cinnamon rolls, on the prepared baking sheet, leaving some space between each roll.
Bake for 18-22 minutes until the pastry has puffed up and turned golden brown. Let the cinnamon rolls cool for five minutes before icing.
Combine the powdered sugar, milk, and vanilla in a small bowl and whisk until smooth. The icing should be the consistency of heavy cream. Add more sugar or milk to adjust if needed.
Drizzle the icing over the cinnamon rolls and serve warm.