Preheat the oven to 350 degrees F.

On a lightly floured work surface, unroll the pastry and, using a floured 2 1/2-inch biscuit cutter, cut the pastry into as many rounds as possible, usually about 25. Brush lightly with the egg wash and place on an ungreased baking sheet. Using a smaller cutter, ideally about 1 1/2-inch wide, make an impression in the center of each round but take care not to cut all the way through the dough. Bake for 12 to 15 minutes, until puffed, golden brown, and cooked through and crispy. Remove from the oven and, using the tip of a paring knife, cut out the center portion of each pastry. Set aside while you assemble the remaining ingredients. (Puffs may be made 1 day ahead and kept in an airtight container at room temperature, then recrisped in a warm oven the day of serving.)

Place the ham on a parchment paper lined baking sheet and cook until crisp, about 10 minutes. Remove from the oven and, once cool, finely chop.

In a small bowl, combine the chopped ham, mascarpone, pesto, salt and pepper and olive oil. Stir gently but thoroughly to blend. Divide the mascarpone filling evenly among the hollowed-out wells in the pastries. Top each pastry with a dollop of the remaining pesto and a Parmigiano-Reggiano shaving. Garnish each with a few pine nuts and serve.