Prepare the Filling: In a mixing bowl, combine pumpkin puree, brown sugar, granulated sugar, ground cinnamon, ground nutmeg, and vanilla extract. Stir until smooth and chill in the refrigerator for 15 to 30 minutes.

Roll Out the Pastry: Roll out each thawed puff pastry sheet into a rectangle of approximately 10x12 inches. Slice each sheet into 6 equal rectangles.

Assemble the Twists: Place a tablespoon of chilled pumpkin filling in the center of each pastry rectangle. Fold over to create a pocket, seal edges, and twist the sealed edges.

Bake: Preheat oven to 400°F (200°C). Arrange twists on a lined baking sheet, brush with egg wash, and bake for 15 to 20 minutes until golden brown.

Cool and Serve: Allow twists to cool on the baking sheet for 5 minutes, then transfer to a wire rack. Enjoy warm.