In a small bowl, mix together the chopped apple, shredded cheddar cheese, and bread crumbs until well combined. Set aside.
Place chicken breasts between two sheets of wax paper and use a meat mallet to gently pound them to 1/4-inch thickness.
Divide the apple mixture evenly between the chicken breasts. Spread the filling across each breast, then roll them up tightly. Secure with toothpicks.
Melt butter in a 7-inch skillet over medium heat. Add the stuffed chicken and cook, turning occasionally, until they are browned on all sides.
Pour in the wine and 1/4 cup water. Cover the skillet and let the chicken simmer gently for 15-20 minutes, or until it is cooked through and no longer pink in the center.
Remove the chicken from the skillet and place it on a serving platter, keeping the juices in the pan.
In a small bowl, stir together 1 tablespoon of water and cornstarch until smooth. Add this mixture to the skillet juices and cook, stirring constantly, until the sauce thickens into a gravy.
Pour the gravy over the stuffed chicken and garnish with freshly chopped parsley before serving.