In a small bowl, toss together the Cheddar cheese and apple. Lay out the pork chops and spread a thin layer of the cheese mixture on top of each one. Roll them up and secure with toothpicks.
Heat the oil in a large skillet over medium-high heat. Quickly brown the outsides of the chops, then pour in the vinegar and water. Reduce heat to low, cover and cook for about 30 minutes.
Mix the flour with a small amount of the liquid from the chops. Stir into the skillet until completely dissolved, then simmer for a few minutes, stirring constantly, to make a quick gravy.