How to Make It
In a large bowl, whisk the mayonnaise with the mustard, olive oil, anchovies and garlic. Add the chicken and toss to coat. Let marinate at room temperature for 20 minutes.
Preheat the broiler and position the rack 6 inches from the heat. Thread the chicken onto skewers and arrange on a large baking sheet. Broil for 8 to 10 minutes, until lightly browned and cooked through. Transfer the skewers to a platter. Sprinkle with grated Parmigiano-Reggiano cheese and serve with lettuce cups and lemon wedges.