Blanche asparagus in a large pot of salted boiling water for about five minutes. Drain, rinse with ice-cold water and place on a kitchen towel to dry.
Mix cream, egg and minced garlic in a small pitcher.
Unwrap and unroll puff pastry, place it on a baking sheet. On the unrolled pastry sheet cut a 1mm-deep slit around the whole perimeter, about 1/2 inch away from the edges (in other words, mark a smaller rectangle wwithin the sheet of puff pastry, cutting only halfway through the thickness). This will be the rim of your tart.
Bake the prepared puff pastry at 400oF for about 5 minutes, until it is all puffy. Take out of the oven and press down the middle of the rectangle, not touching the puffy edges.
Lay slices of prosciutto and then dry blanched asparagus in a single layer on a half-baked puff pastry. Carefully pour egg and cream mixture to cover the asparagus. Sprinkle with Parmesan cheese. Return back to the oven and bake until golden brown.