Brown lamb in a large skillet over medium-high heat until cooked through, 8 to 10 minutes. Remove from heat and carefully tip the skillet to pour off all but about 1 tablespoon of the fat that has accumulated in the pan. Return to heat, add onion and salt and cook until onions are soft and golden brown, 6 to 8 minutes more. Lower heat to medium and stir in currants, oregano, garlic, potatoes and 3 tablespoons water. Cover and cook until potatoes are tender, about 20 minutes more. Remove from heat and mash potato into lamb mixture with a fork. Set aside.
Meanwhile, bring a large pot of salted water to a boil. Working in batches, add chard leaves a few at a time, stirring gently until wilted and just tender, about 30 seconds. Carefully transfer to a paper-towel-lined baking sheet and pat dry. Spoon some of the lamb mixture into the center of each chard leaf and roll up snugly, tucking in the ends. Serve immediately, or refrigerate until ready to serve.
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