Toss the arugula, extra-virgin olive oil and red wine vinegar in a medium mixing bowl until well mixed. Season to taste with salt and pepper and toss again.
Lay 1 slice of prosciutto flat on a cutting board horizontally. Smear with about 1 teaspoon of the mustard (you can use more or less if desired). Line the prosciutto with about 1 tablespoon of the dressed arugula. Wrap the prosciutto-arugula slice around the upper portion of a grissini stick at an angle, slightly overlapping. Repeat for the remaining 11 portions.
Serve standing up in a Mason jar with the prosciutto portion on top.