Bring a large pot of salted water to a boil. Core the cabbage and carefully peel off 12 large outer leaves. Blanch leaves in batches for 2 minutes until pliable. Transfer to ice water, then drain on a towel. Trim the thick center vein from each leaf to make rolling easier.

In a large bowl, mix ground pork, cooked rice, diced onion, minced garlic, beaten egg, salt, pepper, and paprika. Use your hands to combine gently until just mixed - do not overwork or the filling will be tough.

Place a cabbage leaf on your work surface, cupped side up. Add about 1/3 cup filling near the stem end. Fold the sides over the filling, then roll tightly toward the leaf tip, like a burrito. Repeat with remaining leaves and filling.

In the same large pot, whisk together crushed tomatoes, tomato paste, brown sugar, vinegar, and water. Reserve 1 cup of sauce, then spread the rest across the bottom of the pot.

Place cabbage rolls seam-side down in the pot, nestling them snugly in a single layer. Pour reserved sauce over the top. Bring to a gentle simmer over medium heat, then cover and cook on low for 45 minutes until the internal temperature reaches 160°F and the cabbage is tender.

Let rest uncovered for 10 minutes before serving. Spoon sauce from the pot over each portion.