Preheat a panini press or place a large skillet over medium-high heat.
Chop the olives and giardiniera together into a relish. In a small bowl, combine the relish and the EVOO. Spread the relish over one side of the ciabatta.
Layer the meats and cheese over the relish and cap the sandwich off with the other ciabatta half. Slice the sandwich as needed so it fits into the press or pan and grill it until toasted and heated through. If using a skillet, weigh the sandwich down with another pan and flip it over after one side is toasted.
Cut the sandwich up and serve.