Mix the two pestos together and spread over the bottom side of the Naan (bubbly side down).
Top with the shaved parmesan, roasted chicken, toasted pine nuts and arugula.
Place the second Naan, bottom side (not the bubbly charred side) down, on top, pressing the two Naan firmly together. (The "bubbly" side of each Naan should be on the outside of the sandwich.) Place sandwich in preheated panini press, or on hot grill, and toast 4-6 minutes, or until filling is heated through and grill marks appear. Let cool about 1 minute before slicing. Serve immediately.