Preheat the oven to gas 6, 200°C, fan 180°C.
Unroll the sheet of pastry onto a clean board and use a pastry cutter to stamp out 6 x 11cm (4½in) discs. Using a smaller cutter or a knife, lightly score another circle inside the disc to make a border.
Brush with the beaten egg and bake in the oven for 8 minutes, until the pastry is puffed and golden. Leave to cool for 1 minute, and then gently press down the puffed middle to create a hollow space for the filling. Turn the oven down to gas 4, 180°C, fan 160°C.
Meanwhile, blanch the asparagus in a pan of boiling salted water for 2 minutes, then drain and refresh in cold water. Chop the short asparagus stalks into small pieces, leaving the head of the tips whole (put these to one side).
Put a spoonful of crème fraîche in middle of each tart, then add the asparagus stalks and top with the cubes of Camembert.
Add the reserved asparagus tips and finish with the Parma ham strips. Season with black pepper and bake for 6-8 minutes, until the Camembert has melted and the Parma ham is crisp. Serve hot with a leafy salad on the side, if you like.