Bring a large pot of salted water to a boil. Carefully remove the core from the cabbage head and separate the leaves. Blanch the cabbage leaves in the boiling water for about 2-3 minutes until they are pliable. Remove from water and set aside to cool.
In a skillet, heat a small amount of oil over medium heat. Sauté the chopped onion and minced garlic until softened, about 5 minutes. Allow to cool slightly.
In a large mixing bowl, combine the ground beef, cooked rice, sautéed onion and garlic, eggs, salt, pepper, thyme, and parsley. Mix well until all the ingredients are combined.
Take a blanched cabbage leaf and place about 2-3 tablespoons of filling at the base of the leaf. Roll it up tightly, tucking in the sides as you go. Repeat with the remaining leaves and filling.
In a large Dutch oven or stockpot, combine the crushed tomatoes, tomato paste, sugar, and paprika. Add in the chicken or vegetable broth and stir to mix well. Bring to a simmer over medium heat.
Gently add the stuffed cabbage rolls to the pot, making sure they're mostly submerged in the sauce. Cover the pot with a lid and simmer on low heat for about 60 minutes, occasionally checking and basting the rolls with the sauce.
Once cooked, remove the rolls from the pot and serve warm, spooning additional sauce over the top if desired.