Preheat the oven to 425° and line a baking sheet with parchment paper.
Unfold one sheet of puff pastry onto the parchment paper and spread the pesto to cover, then top with Parmesan.
Unfold the second sheet of puff pastry and lay it on top of the other. Gently press to seal.
Cut into a Christmas tree shape (large triangle with small square). Reserve the extra pieces.
With a sharp knife, cut slits on both sides of the tree spacing them about 1/2 inch apart leaving the center (trunk) intact. Twist each strip, pressing the ends onto the baking sheet. Repeat with extra pieces and place on a separate baking sheet.