In a large skillet, heat olive oil over medium heat. Add minced onion and garlic, and sauté until softened.

Add ground beef to the skillet and cook until browned. Drain excess fat.

Stir in Italian seasoning, dill, salt, and pepper, mixing well.

Add marinara sauce and diced tomatoes (with juice) to the mixture, and bring to a simmer.

In a large casserole dish, layer the cooked rice evenly at the bottom.

Add half of the cabbage on top of the rice, then spoon half of the beef mixture over the cabbage.

Repeat the layers with the remaining cabbage and beef mixture.

Dot the top with butter and sprinkle shredded cheese over the entire casserole.

Cover with foil and bake in a preheated oven at 350°F (175°C) for 25 minutes. Remove foil and bake for an additional 10 minutes until cheese is bubbly.