Preheat oven to 425 degrees F; line a baking sheet with parchment paper and set aside.
On a clean surface, using a rolling pin, roll out the puff pastry. Spread a thin layer of pesto/tapenade. Place the salmon in the middle of the pastry and spoon the remaining pesto/tapenade over the top of the salmon.
Fold the edges of the puff pastry over the salmon, starting with the long sides and then the shorter sides. Any excess pastry should be tucked into the side under the pastry log.
Transfer to prepared baking sheet. Brush the beaten egg on the top and sides of the pastry. Using a sharp knife, score the top of the pastry in a crosshatch pattern.
Bake for 25 minutes, until the pastry is golden brown.