For sauce, spray a cold large saucepan with nonstick cooking spray. Add celery, mushrooms, carrot, onion, and garlic. Cook until onion is tender. Cut up tomatoes. Stir undrained tomatoes, tomato sauce, Italian seasoning, and sugar into vegetables. Bring to boiling; reduce heat. Simmer, uncovered, 20 minutes or until mixture is reduced to 2 cups.
Meanwhile, skin, bone, and cut chicken breasts lengthwise in half. Place each chicken piece between 2 pieces of plastic wrap. Pound with a meat mallet to about 1/4-inch thickness.
In a bowl stir together ricotta cheese, Parmesan cheese, and parsley. Spoon about 1-1/2 tablespoons of the cheese mixture on each chicken piece. Fold in long sides of chicken piece, then roll up from short end. Place chicken rolls, seam side down, in an 8x8x2-inch baking dish. Pour sauce over chicken. Cover with foil and refrigerate for 2 to 24 hours.
Before serving, bake, covered, in a 375 degree F oven for 35 to 40 minutes or until chicken is no longer pink. If desired, sprinkle with mozzarella cheese; bake 4 minutes more. Transfer to a platter. Makes 6 servings.