Core the cabbage and place it in a large pot of boiling water. As the outer leaves soften (about 2-3 minutes), carefully peel them off with tongs and transfer to an ice bath. Continue until you have 12-16 large leaves. Trim the thick center rib from each leaf to make rolling easier.
In a large bowl, combine ground meat, cooked rice, diced onion, minced garlic, beaten egg, parsley, salt, pepper, and paprika. Mix gently with your hands until just combined. Over-mixing can make your rolls tough, so stop when ingredients are evenly distributed.
Place about 3 tablespoons of filling near the stem end of each cabbage leaf. Fold the sides inward, then roll from the stem end to completely enclose the filling. The roll should be snug but not so tight that the filling bursts through during cooking.
In a Dutch oven or large pot, combine crushed tomatoes, tomato paste, broth, brown sugar, bay leaf, dill, salt, and pepper. Bring to a gentle simmer, then stir in lemon juice.
Arrange the cabbage rolls seam-side down in the pot with the simmering sauce. Cover and cook on low heat for about 1.5 hours, occasionally spooning sauce over the rolls.