Layer 4 slices cheese over four of the slices of bread.
Top with olive salad, ham, mortadella, salami, remaining cheese and bread.
Cook sandwiches in a preheated panini press until golden brown and cheese is melted, about 3-4 minutes.
Note: Sandwiches may be cooked in a preheated ridged grill pan or skillet over medium heat. Place a heavy skillet on top of sandwiches to flatten; cook 3 minutes. Turn; replace skillet and continue to cook 3 to 4 minutes or until golden brown and cheese is melted.