Bring a large pot of water to a boil. Trim the chard leaves away from their stalks, reserving the stalks for another use (such as Siliq Mutabal). Cut the leaves into 12-by-17-cm (4 ¾-by-6 ½-inch) rectangles or 14-cm (5 ½-inch) squares. Drop into the boiling water and blanche for 20 seconds, then use a slotted spoon to transfer to a bowl of ice water. (Reserve 4 cups/945 milliliters of hot water for the next step.) Remove from the ice water and lay flat to drain on several kitchen towels. Cut chicken into 1-cm (½-inch) cubes, reserving the bones. Boil the chicken cubes and bones in the reserved water for 40 minutes, then strain, reserving 2 cups (500 milliliters) of this chicken stock for the filling. Discard bones (keep remaining stock for another use). Warm the oil in a large skillet over low heat, add the onion and cook for about 10 minutes, until softened. Add the orzo and continue cooking for another 8 to 10 minutes, until lightly toasted. Add the reserved 2 cups chicken stock and the salt and pepper. Cook, uncovered, until the orzo is plump and the liquid evaporated, 15 to 18 minutes. Remove from heat and let cool, then add the dill, chicken, and canned mixed vegetables. This is your filling. Preheat the oven to 170°C (325°F).
Line a short cup or dish (8- to 9-cm/3- to 3 ½-inches in diameter) with 1 or 2 Swiss chard leaves. Put 1 heaping tablespoon of the filling in the center, then fold over the edges of the leaves to enclose. Press with your fingers, so the leaves cover the filling and take the shape of the cup. Turn the cup upside down, and place the stuffed leaves on a tray, flat side down. Repeat with the remaining leaves and filling. Stir ½ cup of olive oil into 3 cups of water, then pour over the stuffed leaves. Drop 1 tablespoon of tomato puree over each of the bundles. Dampen a sheet of parchment paper and place over the stuffed leaves. Bake (middle rack) for 15 to 20 minutes, until the water is almost completely absorbed and the Swiss chard has darkened. Serve hot or cold.