In a medium bowl, combine the ingredients for the olive salad and put to chill in the fridge for at least an hour to blend flavors.
To make the panini, lay 1 slice of bread and spread just a very thin layer mayo (really just to act as a glue). Layer a couple slices ham, some olive salad, a slice of cheese, and the second piece of bread also spread with a very thin layer mayo. Spray the outside sides of bread with olive oil cooking spray.
Heat a panini pan or press (if not available, a large, nonstick skillet can be used, pressing with a spatula to flatten the sandwich a bit). Cook until bread is toasty. Yield: 6 sandwiches.