Remove the core from the cabbage. In a large pot of boiling water, carefully place the head of cabbage with the core hole in the bottom of the pot. Boil and steam the cabbage for 15 to 20 minutes. Remove the head from the pot and carefully peel down one cabbage leaf at a time. You want about 18 large leaves. Set aside the remaining cabbage.
Mix ground meats, egg, onion, cooked rice, salt, pepper, garlic and horseradish in a large bowl.
Place about 1/2 to 3/4 cup of the meat mixture on the widest part of the cabbage leaf. Bring up the bottom of the cabbage leaf over the meat, then tuck the sides over and continue to roll up the entire leaf.
Line a large, heavy pan with some of the extra cabbage leaves that you set aside. Place all the rolls in the cabbage lined pan, and layer as needed. I use a heavy roasting pan that is about 5-inch deep.
In a large bowl, mix undiluted soup, beef broth, brown sugar and vinegar. Pour over rolls.
Cover and bake in a 350°F oven 3-4 hours. The time will vary due to the size of your cabbage leaves. When done, they should be very tender. Add water, if needed to keep the sauce over the cabbage rolls.
Remove the last 30 minutes of cooking.
Notes
If using foil to cover your baking pan, cover the cabbage rolls first with parchment paper. This will keep the acid from the tomatoes from eating holes in the foil, which can give an off-flavor.
Bake on the middle rack of your oven.