Cut the cardoons into julienne about 3-in. long. Cook in boiling water with a pinch of flour and few drops of lemon juice, until tender but stir firm. Drain and pat-dry. Chop the onion and sauté with half the butter. Add the cardoons and let cook gently over low flame for 4 mins. Before removing from the heat, salt to taste. Add some chicken broth if necessary to keep moist. Sprinkle with a pinch of cinnamon; mix in the remaining butter and salt to taste. Top with Parmigiano and serve hot.