Bring a pot of water to a boil and season with salt. Boil cabbage leaves to soften, a couple of minutes. Drain and cool to handle.
In a saucepot over medium heat, melt 2 tablespoons butter and add pasta. Toast to deeply golden and add rice, stir 1 minute, add 2 1/2 cups stock and cook at a simmer for 15 minutes. Cool and reserve.
Melt remaining 2 tablespoons butter in a large, deep skillet over medium heat. Add the meat and lightly brown. Season with salt and pepper; add currants, onions, garlic, nutmeg, dill and parsley. Transfer to a bowl with the rice and stir to combine. To the skillet, add tomato sauce, diced tomatoes and remaining cup stock, and stir to combine.