Sprinkle chicken breasts with 1/4 teaspoon of salt on both sides. Cover and refrigerate for 30 minutes. Remove from refrigerator and cut in half lenghtwise. Place the chicken pieces between two pieces of plastic wrap and pound chicken with meat mallet till 1/4 inch thick.
Preheat oven to 200 degrees F.
Mix the flour, cornstarch, 1 teaspoon of salt, black pepper, and sugar in shallow bowl. Place each piece of chicken into flour mixture to coat. Melt 2 Tbsp of butter in a skillet until foam disappears, and lay the chicken into the butter. Cook until golden brown on both sides. Remove chicken, and set aside on plate in oven to keep warm.
Pour sherry into skillet and bring to a boil, Cook until the sherry is reduced to half its volume. Then stir in chicken broth, add the apple slices to the skillet. Cook, stiring occasionaly until the apple slices are soft and the sherry mixture is reduced to half. Stir in brown sugar, 1 Tsbp of butter, and the Marsala wine until the sugar has dissolved and the sauce is thick.
Return the chicken to the sauce, together with any juice from the plate. Simmer for a few minutes on each side.
Serve the chicken with the sauce and apple slices on top.