Preheat oven to 375F. Remove any tough outer leaves from the cabbage, then cut into quarters through the core. Cut out the core and chop the cabbage into rough 1-inch pieces. You want about 8 cups; don't worry if it's a bit more or less.

Heat a large oven-safe skillet or Dutch oven over medium-high heat. Add the ground beef and cook, breaking it up with a wooden spoon, until it starts to brown, about 5 minutes. Add the diced onion and continue cooking until the beef is fully browned and the onion is softened, about 4 minutes more. Stir in the garlic and cook until fragrant, 30 seconds.

Add the tomato sauce, drained diced tomatoes, uncooked rice, beef broth, Worcestershire sauce, and paprika. Stir well to combine, scraping up any browned bits from the bottom of the pan. The mixture will look soupy; that's exactly right.

Pile the chopped cabbage on top of the beef mixture and press down gently so some liquid comes up through the cabbage. Cover tightly with a lid or foil and bake for 35 minutes. Remove the lid, stir everything together (the cabbage will have wilted significantly), and bake uncovered for another 15 minutes until the rice is tender and most of the liquid is absorbed.

Let the casserole rest for 5 minutes before serving. The sauce will thicken slightly as it sits. Serve hot with a generous dollop of sour cream and a sprinkle of fresh dill.