Preheat oven to 400 degrees Fahrenheit and line a baking sheet with parchment paper.
Whisk together egg and water in a small bowl until smooth and set aside.
In a large bowl, mix canned pumpkin, granulated sugar, and pumpkin pie spice until thoroughly combined.
Divide the pumpkin mixture evenly across each of the four puff pastry sheets, spreading it into an even layer.
Roll each pastry sheet over the pumpkin filling starting from one end, then slice down the center leaving one inch uncut at the top.
Twist the two cut sections together with the filling side facing up and connect the ends to form a circle, pressing to seal.
Place the twisted pastries on the prepared baking sheet spaced apart for expansion.
Brush each twist lightly with the egg wash and sprinkle with coarse sugar if desired.
Bake for 30 to 35 minutes until the pastries are puffed and golden brown.
Allow pastries to cool on the baking sheet for 10 minutes after baking.
Whisk powdered sugar, milk, and vanilla extract in a small bowl until smooth and drizzle the glaze over warm pastries.
Serve immediately for best taste.