In a bowl, combine mayonnaise, dill, and 15 ml (1 tbsp.) lemon juice. Season with pepper and set aside.
In a bowl, toss the arugula with 5 ml (1 tsp.) lemon juice and 10 ml (2 tsp.) olive oil. Season with salt and pepper and set aside.
Cut the buns in half on the horizontal and spread with dill mayonnaise. Add sliced apples, Provolone, and salametti. Top with arugula and close sandwich. Serve immediately.
