In a heavy pot, sweat the onions in olive oil until clear. Stir in the garlic, fire-roasted tomatoes, tomato sauce, and smoked paprika. Simmer for 5 minutes before adding the brown sugar and apple cider vinegar. Let this base concentrate over low heat for 15 minutes.

Submerge the whole cabbage head in a large pot of boiling water for about 8 minutes. Once the leaves look translucent and feel flexible, remove the head and carefully peel away 12 large outer leaves. Trim the thick, woody vein from the bottom of each leaf to make rolling easier.

In a wide bowl, combine the beef, cooked rice, eggs, and herbs. Use your hands to work the spices and rice into the meat until the texture is uniform.

Lay a leaf flat and place a log-shaped portion of meat near the stem end. Fold the sides inward and roll tightly toward the top of the leaf, creating a secure "burrito" shape.

Spread a thin layer of your prepared sauce across the bottom of a 9x13 dish. Arrange the rolls seam-side down to keep them from unraveling. Drown the rolls in the remaining sauce and cover tightly with foil.

Bake at 350°F for 90 minutes. This long, slow braise allows the cabbage to become buttery-soft and the beef to fully infuse with the tomato glaze.