Preheat oven to 350° F.
On a lightly floured surface, roll out the puff pastry to an approximately 11-inch square.
Spread the pumpkin butter evenly in the center of the pastry to form a 4-inch circle.
Sprinkle the walnuts evenly over the pumpkin butter and top with the brie.
Fold the corners of the pastry up over the brie and pinch to seal.
Cut 6 pieces of baker's twine or butcher's twine. Tie each individual piece of twine around the pastry, spacing them evenly apart. Keep the knotted side on the bottom, opposite the smooth pastry side.
Place the pastry-wrapped brie on a baking sheet lined with parchment and brush the top and sides of the pastry with the egg.
Bake for 25-30 minutes or until the pastry is puffed and golden brown.
Remove from the oven and allow to rest for 5 minutes.
Remove the baker's twine and carefully slide the cinnamon stick halfway into the top of the pastry so it sticks out like a pumpkin stem at the top.
Serve warm or at room temperature.