Position a rack in the center of the oven and preheat the broiler. In a bowl, whisk together the lemon juice and anchovy paste. Gradually whisk in the EVOO. Mix in the tuna, celery, onion, basil, olives and capers; season with pepper.
Lightly toast both sides of the bread on a baking sheet under the broiler. Rub one side of each slice with the garlic; cover with a quarter of the tuna salad. Top with the cheese and melt under the broiler.