Heat the oven to 375°F. Bring a large pot of well-salted water to a rolling boil and set a bowl of ice water nearby.
Prep the cabbage: Using a paring knife, remove the core. Lower the whole head into the boiling water. As the outer leaves loosen (about 2–3 minutes), pull them off with tongs and transfer to the ice water. Continue until you have 12–14 pliable leaves. Drain, pat dry, and trim the thick rib on each leaf so it rolls easily without tearing.
Make the sauce: Warm 2 tablespoons olive oil in a medium saucepan over medium heat. Cook the 3/4 cup onion until lightly golden, 5–6 minutes. Stir in the minced garlic, crushed red pepper, cumin, and smoked paprika; cook 30 seconds until fragrant.
Add the fire-roasted tomatoes and tomato sauce, then stir in honey, apple cider vinegar, Worcestershire, salt, and black pepper. Simmer gently, uncovered, for 12 minutes to marry the flavors. Taste and adjust seasoning.
Mix the filling while the sauce simmers: In a large bowl, combine the ground beef, cooked rice, 1/4 cup finely chopped onion, 2 teaspoons minced garlic, oregano, parsley, egg, salt, and pepper. Fold in 2 tablespoons of the warm sauce to moisten. Mix gently with a fork (don’t compact). Cover and chill 10 minutes to firm up.
Lightly oil a 9×13-inch baking dish with 1 teaspoon olive oil. Spread about 1 to 1 1/2 cups of the tomato sauce over the bottom of the dish.
Assemble the rolls: Place a cabbage leaf flat, add about 1/3 cup filling near the base, fold sides in, and roll up snugly. Repeat with remaining leaves and filling.
Nestle the rolls seam-side down in the prepared dish. Spoon most of the remaining sauce over the top, reserving about 1/2 cup for finishing later. Cover the dish tightly with foil.
Bake covered for 65 minutes. Uncover, spoon the reserved sauce over the rolls, and bake 10–15 minutes more, until the cabbage is very tender and the center of a roll reads 160°F on an instant-read thermometer.
Rest 10 minutes before serving. Garnish with extra parsley and ladle any pan sauce over the rolls.