Bring a large saucepan of water to the boil. Cook cabbage leaves in batches, for 2-3 minutes or until bright green. Drain to a tray lined with paper towel. Set aside to cool completely.
Combine mince, garlic, onion, dill, paprika and rice in a bowl.
Cut about 4cm of the thick vein from each cabbage leaf. Place a leaf on a flat surface. Spoon 2 heaped tablespoons of mince mixture along the base of the leaf. Roll up the leaf, folding in the sides to enclose filling. Repeat with remaining leaves.
Heat oil in a large deep frying pan over medium-high heat. Add the rolls in the pan in a single layer. Cook for 2 minutes. Pour over combined tomato puree, 1/3 cup cold water and basil. Bring to a simmer, then reduce heat to low. Cover and simmer for 45 minutes or until the mince is cooked through and rice is tender.
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