1. Wash rice thoroughly. Bring the rice and water to boil in a small or medium saucepan over high heat. Reduce heat to medium-low, cover and simmer until rice is tender and the liquid has been absorbed, 20 to 25 minutes. Allow rice to cool slightly.
2. Meantime, grate the carrot and finely chop the onion and garlic.
3. Remove the core from the cabbage. Carefully separate 9 leaves.
4. Bring a large pot of water to boil, place cabbage leaves in the water, cook 3 minutes. Drain. (You can also freeze the head of cabbage and as it thaws the leaves easily peel away and you don't need to boil them).
5. In a medium skillet, heat the oil, saute onion and carrot for about 5 minutes.
6. In a large bowl, mix together meat, onion, carrot, garlic, and cooked rice. Season the mixture with salt and pepper, stir until well combined.
7. Remove any tough ribs from cabbage leaves using a thin knife. Spoon equal amounts of the meat mixture and rice mixture onto the center of each cabbage leaf. Bring one end of cabbage leaf over mixture, roll tucking ends in to prevent any filling from falling out.
8. In a medium bowl, mix together 2/3 cup sour cream, tomato sauce and water, using enough just to cover the cabbage rolls.
9. Arrange the rolls in a large pot, pour the sour cream and tomato mixture over the top. Cover and bring to boil. Reduce heat to low and simmer, covered, for about 40 minutes.
10. Serve hot, topped with sour cream.