1. With a meat cleaver, poultry shears, or very sharp knife, halve each quail, removing the backbone, or quarter each duckling, if using. Rinse well and pat dry with paper towels.

2. Heat the oil in a Dutch oven over medium heat and brown the birds well on all sides, in batches, if necessary. Set aside. If you are cooking duck, pour off all but 2 tablespoons of fat (quail are leaner and will not release additional fat).

3. Add the onions to the drippings in the Dutch oven and sauté, stirring occasionally, over medium heat for 5 minutes. Stir in the turmeric and continue to cook until the onions turn golden, about 12 minutes.

4. Add the chicken stock and cook, scraping the bottom of the Dutch oven with a wooden spoon, for 3 minutes. Stir in the walnuts and pomegranate juice and heat until the sauce is barely boiling. Reduce the heat to low and simmer the sauce, uncovered, for 20 minutes.

5. Stir in the lemon juice, sugar, cinnamon, cardamom, salt, and pepper. Return the birds to the casserole and mix well to coat with the sauce. Simmer, covered, until the birds are tender, about 30 minutes for quail, 1½ hours for duck.

6. Meanwhile, preheat the oven to 350°F.

7. Uncover the casserole and place in the oven for 15 minutes. Remove and if serving duck, skim off the fat.

8. Serve sprinkled with pomegranate seeds and garnished with mint leaves.