Soften the cabbage: Place the chopped cabbage in a large microwave-safe bowl with 1/4 cup water and a pinch of salt. Cover and microwave on high for 5–7 minutes until just wilted. Drain well and set aside.
Build the meat-and-rice base: Heat a large skillet over medium-high. Add the ground beef and onion, season with 1 tsp kosher salt and 1/4 tsp pepper, and cook, breaking up the meat, until browned, 5–7 minutes. Drain off excess fat. Stir in the garlic and smoked paprika for 30 seconds, then add the uncooked rice and toast for 1 minute. Pour in the Worcestershire, beef broth, and 1 cup of the crushed tomatoes; bring to a lively simmer for 2–3 minutes to start hydrating the rice. Remove from heat.
Preheat the oven to 375°F and lightly grease a 9×13-inch baking dish.
Assemble: Spread half of the wilted cabbage in the baking dish. Spoon the beef-rice mixture evenly over the top. Cover with the remaining cabbage, then pour the rest of the crushed tomatoes over everything, letting it seep around the edges. If the mixture looks dry, drizzle 2 tablespoons water around the sides. Cover the dish tightly with foil.
Bake covered for 40 minutes. Uncover, gently fold the mixture from the edges toward the center to redistribute sauce and cabbage. If the rice still looks firm, add up to 1/4 cup hot water or broth. Re-cover and bake 15–20 minutes more, until the rice is tender and the cabbage is fully soft. Uncover for the last 5 minutes to slightly thicken the sauce.
Rest and finish: Let the casserole stand 10 minutes. Taste and season with the remaining salt and pepper as needed, then serve warm.