In a medium saucepan, over medium heat, melt butter and sauté jalapeño and onion until softened and onions are translucent. Add cherries, wine, vinegar and sugar; cook until cherries are softened and liquid is reduced slightly.
In a small bowl, mix cornstarch with 2 tablespoons of cold water and stir into sauce. Continue stirring until compote thickens slightly, 4 to 5 minutes. Season with salt and pepper.
Meanwhile, grill pork chops until fully cooked; top each with a slice of Fontina and melt. Remove pork chops to individual plates and spoon cherry compote over; serve immediately.