Preheat the oven to 425 degrees F. Lightly grease a baking sheet and set aside.
Unfold the puff pastry sheet on a lightly floured surface. Using a pastry brush, brush the dough with the beaten egg. Sprinkle with the Parmesan and sesame seeds, then roll with a rolling pin to make the cheese and seeds adhere to the pastry. Cut the pastry in half horizontally, then into desired shapes, such as diamonds or rectangles. Transfer to the prepared pan and bake until golden and risen, about 12 minutes. Remove from the oven and serve hot.