How to Make It
Process pine nuts and garlic in a high-speed blender or food processor until roughly chopped, about 30 seconds. Add basil, Parmesan, oil, and salt, and process until well incorporated, about 1 minute, stopping to scrape down sides as necessary. Set aside 2 tablespoons of the pesto. Combine chicken and remaining pesto in a bowl; toss to coat.
Spread each bread slice with 1 tablespoon of the mayonnaise and 1/2 tablespoon of the reserved pesto. Top 2 bread slices evenly with chicken mixture, mozzarella, tomatoes, and arugula. Cover with remaining 2 bread slices. Serve immediately, or wrap with plastic wrap, and chill until ready to serve, up to 2 days.