Arrange the top oven 4" to 6" from the top heating unit, and preheat broiler to high. Line a rimmed baking sheet with parchment paper or a silpat mat (for easy cleanup).

Slice the prosciutto in half lengthwise; you'll use one half for each breadstick.

Sprinkle a big pinch of grated cheese over the prosciutto, followed by a pinch each of basil and oregano.

Leaving 2" at the tip, roll up the breadstick in the prosciutto, pulling tightly, but without tearing the prosciutto. There should be 3" to 5" of exposed breadstick at the bottom, to use as a sort of handle.

Continue wrapping the remaining the breadsticks.

Place the wrapped breadsticks on the prepared pan, and place under the broiler. Do not walk away! Remove from oven when the prosciutto is sizzling lightly, but before the exposed breadsticks begin to brown, just a few minutes.

Serve immediately.

The prosciutto-wrapped breadsticks can be assembled an hour or so ahead of time and refrigerated. Broil before serving.