1. Preheat oven to 350°.
2. Heat a large Dutch oven over medium heat. Add oil to pan; swirl to coat. Add onion, carrot, and celery; sauté 6 minutes. Add rice and garlic; cook 3 minutes, stirring to coat rice with oil. Spoon rice mixture into a large bowl; crumble sausage and beef into bowl. Add parsley, 1/2 teaspoon pepper, and egg; stir well.
3. Steam cabbage leaves, covered, 6 to 8 minutes or until tender and pliable. Remove cabbage from steamer. Let cool slightly.
4. Working with 1 cabbage leaf at a time, place about 1/2 cup meat mixture in center of leaf. Fold in edges of leaf; roll up. Repeat procedure with remaining cabbage leaves and meat mixture to form 18 cabbage rolls; set aside.
5. Combine crushed tomatoes, broth, brown sugar, salt, and remaining 1/4 teaspoon pepper in Dutch oven; bring to a simmer over medium, and cook 15 minutes, stirring occasionally. Remove from heat. Add cabbage rolls to pan, nestling them into sauce and spoon sauce over rolls. Cover pan with lid, and bake at 350° for 1 1/2 to 2 hours or until rice is tender and meat mixture is no longer pink. Serve sauce over cabbage rolls.