Cook rice according to directions on package. Set aside.
Empty stewed tomatoes into a saucepan & squeeze or cut-up to desired size, removing any hard cores/bad spots. Add tomato soup, salt, pepper, sugar & parsley. Let simmer uncovered on low, stirring occasionally.
Remove some of the cabbage core with a sharp knife and set cabbage in a large pot. Add water to cover & add vinegar. Cover and bring to a boil.
Cook for 10 minutes until outside leaves can be removed, being careful not to tear them. The leaves need to be pliable enough to roll them up, but not cooked through. Set leaves on a plate as they are removed. Continue cooking & removing more leaves. Small remaining leaves can be used to make Haluski.
In a large bowl, mix the hamburger, cooked rice, salt & pepper and ½ to 1 cup of the tomato mixture until just mixed. The tomato mixture is to give it some flavor and loosen it up, don't add too much.
Put a thin layer of the tomato mixture in a 9x13 baking dish & set aside. Lay out one cabbage leaf & put 1/4 to 1/2 cup hamburger mixture toward the core end. Roll the core end over the hamburger, tuck in each side & continue to roll the leaf to the end. Set in baking dish as you roll them, large rolls outside, small rolls inside. Repeat with remaining leaves. Preheat oven to 350F.
Pour the remaining tomato mixture over cabbage rolls. Cover the casserole with a lid or foil. Bake for 1-1/2 to 2 hours until tender. The longer they bake the better, maybe up to 2-1/2 hours.