Preheat the broiler.
In a large bowl, combine the anchovy paste with extra-virgin olive oil. Add the olives, onions, celery, tuna, lemon juice and pepper, to taste, and toss to combine. Lightly butter each side of the rolls, and toast on each side under the broiler. Fill the rolls with the tuna salad and top with cheese. Arrange on a sheet pan and broil until the cheese melts. Transfer to serving plates and serve.