Cut the peaches in half and remove the seeds. Cut up the peaches into 1/2-inch slices. Take the haloumi and using a sharp knife (haloumi is pretty firm), slice it up into rectangles.
Preheat your grill or grill pan over high heat. Grease it with cooking spray, liberally (you don't want the cheese and fruit to stick). While the grill or grill pan is preheating, add the arugula to a small bowl. Pour in the olive oil and add a teaspoon of salt. Rub the leaves until they're thoroughly coated. Set them aside.
In a small saucepan, set over medium heat, add the balsamic vinegar. Bring the mixture to a simmer and then turn the heat down to low. Allow the balsamic vinegar to reduce by half; make sure to keep a close eye on it---it reduces very quickly. Pour the balsamic glaze into a small bowl; it will thicken as it cools.
Add the fruit to the grill. To get those pretty grill marks, lightly press the fruit down with a pair of tongs. Cook for about 1 minute on the first side and 30 seconds on the opposite side. Repeat grilling process until you've worked your way through all of the fruit, adding extra cooking spray as needed.
Next, add the haloumi (you want to do the haloumi last because it's important that's it's as melty as warm as can be) and place a flat lid or plate on top of the haloumi. This will help with those perfect grill marks. Grill the cheese for about 2 minutes per side.
Arrange the grilled peaches, grilled haloumi, dressed arugula leaves and prosciutto on a large plate. Drizzle the balsamic glaze on top and around the salad.