In a medium saucepan, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, approximately 3–4 minutes. Stir in the minced garlic and cook for an additional 30 seconds. Incorporate the fire-roasted diced tomatoes (with liquid), tomato sauce, brown sugar, red wine vinegar, and red pepper flakes. Season with salt and black pepper. Bring the mixture to a gentle boil, then reduce heat to low and simmer, covered, for 15 minutes. Set aside.

Fill a large stockpot approximately three-quarters full with water and bring it to a boil. Carefully lower the entire head of cabbage into the boiling water. Boil for about 8 minutes or until the outer leaves are pliable. Remove the cabbage from the water and rinse under cold water to halt the cooking process. Gently peel off 12 large outer leaves. Trim the thick vein from each leaf to allow easier rolling.

In a large mixing bowl, combine the ground beef, cooked white rice, chopped onion, parsley, eggs, cumin, Italian seasoning, salt, and pepper. Mix thoroughly until all ingredients are well incorporated.

Divide the meat mixture into 12 equal portions. Place one portion in the center of each cabbage leaf. Fold the sides inward and roll tightly to enclose the filling, forming a compact roll.

Preheat the oven to 350°F (175°C). Spread half of the prepared tomato sauce in the bottom of a 9x13-inch baking dish. Arrange the cabbage rolls, seam-side down, over the sauce. Pour the remaining sauce over the rolls, ensuring they are well covered. Cover the dish with aluminum foil and bake for approximately 90 minutes, or until the cabbage is tender and the filling is fully cooked through.