Carefully separate the leaves from the thawed cabbage head, ensuring they remain intact for easy wrapping.

In a large mixing bowl, combine the lean ground beef, ground pork, and ground ham. Add the uncooked rice, finely chopped onion, egg, salt, black pepper, and garlic powder. Mix thoroughly until all ingredients are evenly distributed, creating a well-blended filling. Shape the meat mixture into oval-shaped portions, using roughly ½ cup for each. Lay a cabbage leaf flat and tightly wrap it around the filling, tucking in the sides to form a secure roll.

Spread the sauerkraut evenly across the bottom of a heavy, large pot to create a tangy bed for the cabbage rolls. Arrange the stuffed cabbage rolls over the sauerkraut, placing them seam-side down to prevent them from unraveling during cooking.

Once all rolls are positioned, pour the tomato juice evenly over the top, allowing it to seep into the layers. Add enough water to cover the rolls completely. Set the pot over high heat and bring to a gentle boil. Once boiling, reduce the heat to low and simmer uncovered for approximately 3 hours. Keep an eye on the pot, adding more water if necessary to ensure the rolls stay submerged and cook evenly, resulting in tender cabbage and a richly flavored filling.