Cut the zucchini in half lengthwise and remove the ends.
Cut each half lengthwise into 1/4″ (0.5 cm) thick slices. Cut each slice into 1/4″ (0.5 cm) thick sticks and discard the central part where the seeds are, so that each stick has skin.
You should have about 36 sticks.

Lay out the samosa pastry sheets on a work surface and brush them lightly with butter.
Sprinkle the samosa pastry sheets with parmesan in a uniform layer.
Place a few pieces of prosciutto across one short side of each pastry strip, about 1″ (2.5 cm) from the bottom edge.
Place 1 zucchini stick on the prosciutto, leaving the ends hanging out of the pastry strip on either side.
Roll like a rolled cake and brush the top of the pastry and the protruding zucchini lightly with butter.
Place, seam-side down, on a baking sheet lined with parchment paper, at least 1/2″ (1 cm) apart.
Do the same with the remaining samosa pastry sheets and ingredients.
(These sticks can be stored in the refrigerator, covered with plastic wrap, for 1 day.)

To serve, preheat the oven to 450 F (230 C).

Bake for about 8 to 10 minutes or until the pastry is golden brown and crispy.
Serve immediately.