In a medium saucepan, combine 1 cup of rinsed basmati rice, 2 cups of water, and ½ teaspoon salt. Cook on low heat for about 15 minutes, or until the water has evaporated and the rice is tender. Remove from heat and let it cool completely.

In a large skillet, heat 2 tablespoons of olive oil and 1 tablespoon of butter over medium heat. Add 1 finely minced onion and 1 grated carrot, sauté for about 5 to 7 minutes until translucent. Set aside to cool slightly.

Combine the cooled rice, sautéed vegetables, 1 pound of ground pork, ¼ cup of chopped parsley, 1 teaspoon of salt, and ½ teaspoon of black pepper in a mixing bowl. Mix gently until combined.

Core the cabbage head, bring a large pot of salted water to a boil, and blanch the cabbage leaves for 2 to 3 minutes until flexible. Transfer leaves to a plate to cool.

Trim thick stems from softened cabbage leaves. Place filling at the base of each leaf, roll tightly, tucking in the sides. Arrange on a tray.

In a large pot, layer sliced carrots and leftover cabbage leaves at the bottom. Arrange cabbage rolls on top, intersperse with tomato sauce and sour cream.

Cover pot with water to just cover the top layer of rolls, cover with a lid, and simmer on low heat for about 1 hour. Remove from heat and rest covered for 15 minutes before serving.