Bring a large pot of water to a boil. Carefully core the cabbage and place it in the boiling water. Cook for 5-7 minutes, or until outer leaves peel away easily. Remove 12 large leaves and set aside. Trim thick stems to flatten.

In a large skillet, cook ground beef over medium heat until browned. Drain excess fat. Add onion and garlic; cook for 3-4 minutes until softened.

Stir in uncooked rice, beaten egg, salt, and pepper. Mix well and remove from heat. Let cool slightly.

Place about 2 tablespoons of filling near the stem end of each cabbage leaf. Fold sides over filling, then roll up tightly. Repeat with remaining leaves and filling.

In a large pot or Dutch oven, combine crushed tomatoes, tomato sauce, beef broth, brown sugar, oregano, and paprika. Stir well.

Arrange cabbage rolls seam-side down in the pot, stacking them tightly. Pour sauce over rolls until mostly covered.

Bring to a simmer, then cover and reduce heat to low. Cook for 1.5 hours, or until rice is tender and filling is cooked through.

Serve hot, spooning extra sauce over each serving.