With the rack in the middle position, preheat the oven to 180 °C (350 °F).
In a bowl, combine the meat, onion, garlic, and spices. Season with salt and pepper.
Crumble half the meat mixture into a 33 x 23-cm (13 x 9-inch) baking dish. Sprinkle with half the rice and cover with half the tomatoes. Layer with half the cabbage and press gently. Add the remaining meat and rice in the same way. Cover with the remaining tomatoes. Layer with the remaining cabbage. Season with salt and pepper. Add the broth. Cover with a sheet of aluminum foil. Bake for 2 hours. Remove the foil and bake for 30 minutes.