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. Cut tops off peppers, remove seeds and white membranes. Rinse peppers under cold water. Bring a large pot of water to boil, place peppers in the water, cook 3 minutes. Drain and set aside.
3. Grate the carrot, finely chop the garlic and onion.
4. In a medium skillet, heat the oil, saute onion and carrot for about 5 minutes.
5. In a bowl, mix together meat, rice, carrot, onion and garlic. Season the mixture with salt and pepper, stir until well combined.
6. In another bowl, mix together 2/3 cup sour cream, tomato sauce and water, using enough just to cover the peppers.
7. Stuff each pepper with the beef and rice mixture.
8. Place the peppers open side up in a pot, pour the sour cream and tomato mixture over the stuffed peppers. Cover and bring to boil. Reduce heat to low and simmer, covered, for about 40 minutes.
9. Serve hot, topped with sour cream.