Preheat oven to 375°F (190°C).

Roll the thawed puff pastry into a very thin rectangle on a lightly floured surface.

Sprinkle with the grated Parmigiano-Reggiano cheese and freshly ground black pepper.

Arrange the thinly sliced prosciutto over the cheese to cover the entire surface.

Cut the pastry into 3-inch triangles using a pizza cutter.

Roll each triangle up from the wide end, enclosing the cheese and prosciutto filling.

Arrange the rolled pastries on a baking sheet and shape them into crescents.

Brush the tops of the crescents with the beaten egg.

Sprinkle the brushed crescents with the grated Grana Padano cheese.

Bake in the preheated oven for 20 minutes, or until golden brown and crisp.