In a mixing bowl, combine the pumpkin puree, brown sugar, granulated sugar, cinnamon, nutmeg, and vanilla extract until smooth. Cover and chill for about 15-30 minutes.

Roll out each sheet of puff pastry to approximately 10 by 12 inches and cut into six rectangles, each 4 by 5 inches.

Place about a tablespoon of pumpkin filling in the center of each rectangle, fold and seal tightly, then twist for shape.

Preheat the oven to 400°F (200°C). Whisk together the egg and water for the egg wash and brush each twist.

Bake the twists for 15-20 minutes or until golden brown. Keep an eye on them for a perfect finish.

Let the twists cool on a wire rack for about 5 minutes before serving. Enjoy warm with powdered sugar or icing.