For the Aioli: Place all the ingredients, except the salt and pepper, in the bowl of a food processor. Blend until the mixture is smooth. Transfer the aioli to a medium bowl. Season with salt and pepper.
For the Sandwich: Add the shredded chicken to the aioli and mix well. Preheat a heavy-bottomed skillet over medium heat. Using tongs, add the tortillas, 1 at a time, and cook until warm, about 30 seconds each side. Place the warm tortillas on a work surface and spread with the chicken mixture, leaving a 1/2-inch border. Sprinkle the arugula over the chicken mixture. Carefully roll up the tortillas, jelly-roll fashion. Cut each rolled sandwich in half, diagonally, and transfer to a serving platter. Serve.
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Rolled Chicken Sandwich With Arugula and Parsley Aioli (cont.)