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

On a lightly floured surface, roll out each sheet of puff pastry to approximately 10x12 inches and slice into 6 rectangles.

Place 1 tablespoon of chilled pumpkin filling in the center of each pastry rectangle and form a pocket by folding and sealing the edges.

Preheat the oven to 400°F (200°C) and brush the twists with an egg wash before arranging on a lined tray.

Bake for 15-20 minutes or until golden brown, then cool for a few minutes before serving.