Prepare the cabbage leaves: Bring a large pot of water to a boil. Carefully remove 8-10 large cabbage leaves from the head and blanch them in the boiling water for 2-3 minutes, until softened. Drain and set aside.
Make the meat filling: In a large bowl, combine the ground beef or lamb, onion, garlic, cauliflower rice (if using), egg, parsley, thyme, salt, and pepper. Mix well.
Assemble the cabbage rolls: Place a spoonful of the meat mixture into the center of each cabbage leaf. Fold in the sides and roll up tightly, tucking in the ends.
Prepare the tomato sauce: In a saucepan, combine the crushed tomatoes, beef broth, tomato paste, oregano, salt, and pepper. Bring to a simmer and cook for 5-7 minutes, stirring occasionally.
Bake the cabbage rolls: Preheat the oven to 350°F (175°C). Spread a small amount of the tomato sauce on the bottom of a baking dish. Place the cabbage rolls seam-side down in the dish and pour the remaining sauce over them. Cover the dish with foil and bake for 45-50 minutes, until the meat is cooked through and the cabbage is tender.
Serve: Serve hot, garnished with extra parsley if desired.