Heat the oil in a large skillet over medium heat.
Sprinkle pork chops with salt and pepper. Add to the pan and cook until browned, approximately 4 minutes per side. Transfer to a plate.
Add the prosciutto and cook until browned, or about 1 minute. Transfer to the plate with the chops.
Add the cider, ½ cup of broth, both gingers, vinegar, sage and apple to the pan. Bring to a boil on medium high heat, then reduce to a simmer and cook until the apples are soft, approximately 6 minutes.
Stir together the remaining broth and cornstarch in a small bowl and add to the skillet. Bring to a simmer, stirring continually.
Add back the pork and prosciutto and simmer for 4 to 6 minutes or until pork is fully cooked. Turn once or twice to cover chops with the sauce.
Serve with plenty of sauce spooned over the chops.