Remove core from cabbage. Place whole head in a large pot filled with boiling, salted water. Cover and cook 3 minutes, or until softened enough to pull off individual leaves. You will need about 18 leaves.
When leaves are cool enough to handle, use a paring knife to cut away the thick center stem from each leaf, without cutting all the way through. Chop the remaining cabbage and place it in the bottom of a Dutch oven or large saucepan along with the copped carrot.
Saute chopped onion, and bell pepper in butter in a large skillet until tender, and let cool.
In a large bowl, mix cooked rice, cooled onion mixture, meat, garlic, egg, and salt and pepper until well combined.
Place about 1/2 cup of meat on each cabbage leaf. Roll away from you to encase the meat. Flip the right side of the leaf to the middle, then flip the left side. You will have something that looks like an envelope. Once again, roll away from you to create a neat little roll.
Place the cabbage rolls on top of the chopped cabbage in the Dutch oven, seasoning each layer with salt and pepper. Combine tomato sauce with beef or chicken stock and pour over rolls. Bring to a boil, cover, reduce heat and simmer on the stovetop for 1 hour.
Serve with pan juices and a drizzle of sour cream, or mix the pan juices with sour cream and ladle it over the cabbage rolls.
Cabbage rolls freeze well, and can also be made in a slow cooker