Remove the outer leaves from the head of cabbage and place the whole cabbage in the freezer. After 2 days, transfer the head of cabbage to the fridge and let it thaw, preferably overnight. Once thawed, gently unfold the softened cabbage leaves, leaving them attached to the intact core.
For the ground beef filling, combine the ground beef, cooked rice, diced onions, minced garlic, and eggs and season with cumin, marjoram, salt, and pepper.
Starting with the innermost leaves, coat each cabbage leaf with a thin layer of the ground beef filling and push the coated cabbage leaf against the core in the center. Continue coating the cabbage leaves and folding them back up, working from the inside out.
For the sauce, heat some olive oil over medium heat in an oven-proof skillet and sauté the chopped vegetables. Add the tomato paste and sugar and cook everything together briefly. Pour in the red wine and let it reduce by about half. Add the broth and let the sauce come to a boil.
Place the stuffed cabbage head in the skillet with the sauce, transfer the skillet to a preheated oven, and cook at 325°F for 1 hour.
