Warm olive oil over medium-high heat in a saucepan. Add the finely diced onion and cook until softened, about 2 minutes. Incorporate the garlic and stir until aromatic. Introduce the fire-roasted tomatoes, tomato sauce, crushed red pepper, salt, and pepper. Stir well and allow to cook for 5 more minutes. Blend in the brown sugar and vinegar, then bring the mixture to a gentle simmer. Continue simmering for 15 minutes, stirring regularly.

In a large pot, bring water to a low boil. Gently place the whole cabbage into the boiling water and let it cook for 7–8 minutes, or until the outer leaves become pliable. Remove from water and let cool slightly on a tray. Detach 12 leaves carefully.

In a large bowl, combine ground beef, cooked rice, diced onion, minced garlic, salt, pepper, Italian seasoning, parsley, and eggs. Mix thoroughly by hand until the filling is evenly blended.

Lay each cabbage leaf flat and trim the thick vein at the base. Take a portion of the meat mixture, shape it into a log, and place it at the center of the leaf. Fold the sides inward and roll up tightly, forming a sealed bundle. Repeat with the remaining filling and leaves.

Spread half of the prepared tomato sauce across the base of a 9×13-inch baking dish. Arrange the cabbage rolls seam-side down in the dish. Spoon the remaining sauce over the rolls, ensuring they are at least half-covered. Cover tightly with foil.

Bake in a preheated oven at 350°F for 60 minutes, until thoroughly cooked and the flavors have melded.