1) Prep the cabbage leaves
Bring a large pot of water to a gentle simmer (not a rolling boil). Remove the cabbage core by cutting a deep cone around it, then pull the core out. Lower the whole cabbage into the pot. Simmer for 4 to 6 minutes to start, then use tongs to peel off softened outer leaves as they loosen.
Keep simmering and removing leaves as needed until you have about 12 good leaves. (Some cabbages cooperate fast, others need closer to 8 to 15 minutes total with leaf-by-leaf removal.) Lay leaves on a tray and let cool.
With a knife, trim the thick rib on each leaf by shaving it down (do not cut the leaf in half). This is the secret to easy rolling.
If you are short on large leaves: Use smaller leaves for smaller rolls, or overlap two small leaves to patch one roll. You can also line the bottom of the baking dish with extra cabbage leaves to prevent sticking.
2) Par-cook the rice
Cook rice in lightly salted water until it is about halfway cooked, 6 to 8 minutes for most white rice. It should still have a firm bite. Drain and cool.
3) Make the filling
Heat olive oil in a skillet over medium heat. Sauté onion for 4 to 5 minutes until soft, then add garlic for 30 seconds. Scrape into a large bowl and let cool slightly.
Add pork, beef, par-cooked rice, egg, parsley, paprika (if using), black pepper, and 1 teaspoon kosher salt. Mix gently with your hands until just combined. Do not overwork it.
4) Make the sauce
In a saucepan, heat olive oil over medium heat. Add onion and cook 4 minutes, then add garlic for 30 seconds. Stir in crushed tomatoes, tomato sauce, brown sugar, vinegar, oregano, 1/2 teaspoon kosher salt, and pepper. Simmer 10 minutes. If it feels too thick, add a splash of water or broth until it is nicely spoonable. Taste and adjust salt, sweetness, and tang as you like.
5) Roll and assemble
Heat oven to 350°F. Spread about 1 cup of sauce in the bottom of a 9x13-inch baking dish.
Place a cabbage leaf on your board. Add about 1/4 to 1/3 cup filling near the bottom (use less for smaller leaves). Fold the sides in, then roll up snugly like a burrito. Place seam-side down in the baking dish. Repeat, packing rolls close together.
6) Bake
Pour remaining sauce over the rolls. Cover tightly with foil (or a lid). Bake 60 minutes. Uncover and bake 15 to 20 minutes more until bubbling and slightly thickened.
For the most reliable doneness check, the filling should reach 160°F in the center of a roll. Rest 10 minutes before serving. Spoon sauce over the top and taste for salt.
