Pour the oil in a pot. Once heated, add the grated carrot to braise it. Add the finely chopped leeks and the mince.
Braise well and pour in the rice. Once it's braised and turns glassy, add the paprika. Pour in about 1 cup of water and boil until the water's absorbed.
Season with the spices. Put 1 tbsp of the mixture in each cabbage leaf and wrap it up. Arrange them in a buttered, deep oven dish. Pour on a little oil, cover with cabbage leaves on top.
Top the oven dish with water to cover the sarma and bake at 356°F (180 °C) for about 1 hour, until the rice softens.