Preheat the oven to 350°F (175°C).
Bring a large pot of water to a boil. Carefully core the cabbage and place the whole head in the boiling water for about 5 minutes, or until the outer leaves are pliable. Remove the cabbage and peel off 12 large leaves. Set aside to cool.
Trim the thick vein from the base of each cabbage leaf to make rolling easier.
In a large bowl, combine the ground beef, cooked rice, chopped onion, minced garlic, egg, salt, black pepper, dried parsley, and dried thyme. Mix well until all ingredients are evenly incorporated.
Place a cabbage leaf on a flat surface. Put about 2 tablespoons of the meat mixture near the base of the leaf. Fold the sides over the filling and roll tightly from the base to the tip to form a neat roll. Repeat with remaining leaves and filling.
In a large ovenproof dish, heat olive oil over medium heat. Pour in tomato sauce and beef broth, stirring to combine.
Arrange the cabbage rolls seam side down in the sauce in a single layer.
Cover the dish with aluminum foil and bake in the preheated oven for 1 hour, until the meat is cooked through and the cabbage is tender.
Remove from the oven and let rest for 10 minutes before serving.