Bring a large pot of water to a gentle boil. Remove the core from the head of cabbage and carefully submerge it in the water. Peel away 12 to 15 leaves as they soften, setting them aside to cool. Trim the thick center vein from each leaf to make rolling easier.

In a large bowl, combine the ground meat, cooked rice, diced onion, minced garlic, beaten egg, parsley, paprika, salt, and black pepper. Mix until the ingredients are fully incorporated, but avoid overmixing to keep the filling tender.

Place about 2–3 tablespoons of the meat mixture near the base of each cabbage leaf. Fold in the sides and roll tightly from the bottom up, forming a compact bundle. Repeat until all the filling is used.

In a deep skillet or large saucepan, heat olive oil or butter over medium heat. Sauté the chopped onion for 3–4 minutes, or until softened. Add the minced garlic and cook for 30 seconds more.

Stir in the tomato paste and cook for 1 minute to deepen the flavor. Pour in the crushed tomatoes, followed by the sugar, paprika, oregano or seasoning blend, salt, pepper, and broth. Bring the sauce to a simmer.

In a large Dutch oven or deep baking dish, spread a thin layer of the tomato sauce on the bottom. Arrange the cabbage rolls seam-side down in a single or slightly overlapping layer. Pour the remaining sauce evenly over the rolls.

Cover the pot or dish tightly with a lid or foil. Simmer gently on the stovetop over low heat for about 1 hour and 30 minutes, or bake at 350°F (175°C) for the same duration, until the cabbage is very tender and the filling is fully cooked.