Start by peeling and removing the core from the cabbage. Fill a large pot with water and bring it to a boil. Once boiling, carefully place the cabbage head in the pot and blanch for about 5 minutes until the outer leaves are tender. Remove the cabbage, let it cool, and gently peel off the leaves. Set aside about 12-15 leaves for stuffing.
In a skillet over medium heat, add a splash of olive oil and sauté the chopped onion and minced garlic until softened, about 5 minutes. Remove from heat and let cool slightly.
In a mixing bowl, combine the ground beef (or turkey), cooked rice, sautéed onion and garlic, egg, salt, pepper, thyme, and oregano. Mix well until fully combined.
Preheat your oven to 350°F (175°C).
To assemble the rolls, take a cabbage leaf and place about 2-3 tablespoons of the filling at the base of the leaf. Fold in the sides and roll it up tightly from the base to the top. Repeat until all the filling is used.
Spread a thin layer of the crushed tomatoes on the bottom of a baking dish. Place the stuffed cabbage rolls seam-side down in the dish. Once all the rolls are arranged, pour the remaining crushed tomatoes over the top.
In a small bowl, mix together the tomato paste and sugar with the beef broth. Pour this mixture over the cabbage rolls.
Cover the baking dish with aluminum foil and bake in the preheated oven for 45 minutes. After that, remove the foil and bake for an additional 15 minutes to brown the top.
Once done, let the cabbage rolls rest for about 10 minutes before serving.