Preheat the oven to 350°F (175°C).
Bring a large pot of water to a boil. Core the cabbage and carefully separate the leaves. Blanch the cabbage leaves in boiling water for 2-3 minutes until pliable. Drain and set aside to cool.
In a large skillet, heat the vegetable oil over medium heat. Add the chopped onion and cook until softened, about 5 minutes. Add the minced garlic and cook for 1 minute more. Remove from heat and let cool slightly.
In a large mixing bowl, combine the ground beef, cooked rice, sautéed onion and garlic, egg, salt, black pepper, paprika, and dried thyme. Mix thoroughly until well combined.
Place a cabbage leaf on a flat surface. Trim the thick vein at the base of the leaf if necessary to make rolling easier. Place about 1/4 cup of the meat mixture in the center of the leaf. Fold the sides over the filling and roll up from the base to enclose the filling completely. Repeat with remaining leaves and filling.
In a baking dish, spread a thin layer of tomato sauce and crushed tomatoes mixed with water.
Arrange the cabbage rolls seam side down in the baking dish. Pour the remaining tomato sauce over the rolls, covering them evenly.
Cover the dish tightly with aluminum foil and bake in the preheated oven for 1 hour.
Remove the foil and bake for an additional 15 minutes to allow the sauce to thicken slightly.
Remove from oven and let cool for 10 minutes before serving.