Preheat your oven to 180°c (160°c for fan assisted ovens or Gas Mark 3) and line a baking tray with greaseproof paper.
In a bowl, mix together the butter, sugar & cinnamon until well combined.
Roll out your puff pastry and keep it on the enclosed paper. Don't worry about uneven edges as these will be neaten off shortly.
Use a spoon to gently spread the cinnamon filling all over the pastry, leaving a 1cm gap at the edge of one of the longest sides.
Using the puff pastry's enclosed paper, gently roll the pastry into swirls, leaving the 1cm gap to seal the swirls by lightly pressing them in place.
With a sharp knife, cut the pastry into sections around 2cm thick, whilst trimming the ends of the pastry to keep each cinnamon swirl even & neat. Place each swirl onto the pre-lined baking tray with a bit of space between them as they do expand whilst baking
Use the beaten egg to lightly coat each swirl and sprinkle a little sugar over them. Leave them to rest for around 20-30 minutes.
Bake in the preheated oven for 20 minutes or until golden brown. Meanwhile, in a small bowl, mix the icing sugar with a little warm water to create your icing to drizzle on top of your cinnamon swirls.
Remove the cinnamon swirls from the oven and whilst still warm and on their baking tray, drizzle the icing over them (using as much or as little as you like).
Once cool enough to touch, transfer to a wire rack to cool completely or tuck right in.