Bring a large pot of salted water to a rolling boil. Cut a circle around the cabbage core and remove it, going about 2 inches deep.
Lower the whole head of cabbage into the boiling water, core side down. Boil for 3 to 4 minutes, then use tongs to peel away the outer leaves as they soften.
Continue peeling leaves in layers, returning the cabbage to the water for another minute or two between rounds, until you have at least 12 large, flexible leaves. Lay the leaves on a clean kitchen towel to drain and cool slightly.
Using your paring knife, shave down the thick rib at the base of each leaf so it folds easily without cracking.
Melt 1 tablespoon of the butter in a small skillet over medium heat. Add half of the diced onion and cook for 3 to 4 minutes, stirring occasionally, until soft and translucent.
Add the minced garlic and cook for another 30 seconds, just until fragrant. Remove the skillet from the heat and let the mixture cool for a few minutes before adding it to the filling.
In a large mixing bowl, combine the ground beef, Italian sausage, cooked rice, cooled onion and garlic mixture, egg, parsley, 1 teaspoon of the salt, black pepper, and smoked paprika.
Use your hands to gently mix everything together just until combined. Overmixing can make the filling tough, so stop as soon as the ingredients are evenly distributed.
In the same skillet used for the onions, melt the remaining tablespoon of butter over medium heat. Add the remaining diced onion and cook for 3 to 4 minutes until softened.
Stir in the San Marzano crushed tomatoes, tomato sauce, brown sugar, apple cider vinegar, Worcestershire sauce, and the remaining 1/2 teaspoon of salt.
Bring the sauce to a gentle simmer and cook for 8 to 10 minutes, stirring occasionally, then remove from the heat.
Preheat your oven to 350 degrees Fahrenheit.
Spoon about 1/3 cup of the meat filling onto the center of a cabbage leaf, near the base where the rib was trimmed. Fold the sides of the leaf in over the filling, then roll it up tightly from the base to the tip, like a burrito.
Repeat with the remaining leaves and filling. If some leaves tear, you can double them up or patch small holes with a second small leaf.
Spread a thin layer of the tomato sauce across the bottom of your 9x13 inch baking dish. Arrange the cabbage rolls seam side down in a single snug layer.
Pour the remaining tomato sauce evenly over the top of the rolls. Cover the dish tightly with aluminum foil.
Bake for 1 hour and 15 minutes, then check the internal temperature of a roll with your meat thermometer. It should read at least 165 degrees Fahrenheit.
If needed, uncover and bake for another 10 to 15 minutes to let the sauce reduce slightly.
Let the rolls rest for 10 minutes before serving so the filling has time to set.