Spread some butter over 4 inches of 1 end of each breadstick. Spread Parmesan cheese on plate. Roll buttered end of each breadstick in cheese to coat lightly. Place 1 slice prosciutto on work surface; arrange 3 arugula leaves atop prosciutto, then place cheese-covered end of breadstick atop arugula and roll up prosciutto around breadstick, enclosing arugula. Repeat procedure with remaining breadsticks. (Can be prepared 2 hours ahead. Place breadsticks in tall glass, prosciutto ends up. Cover with plastic wrap and chill.) Tuck 2 arugula leaves into prosciutto end of each breadstick and serve.

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