Heat the vegetable oil in a large pot over medium heat. Add the chicken pieces and brown them on all sides. Remove the chicken and set aside.
In the same pot, add the chopped onions and cook until they are soft and golden brown, about 8-10 minutes.
Add the ground walnuts, ground cinnamon, turmeric, and cardamom to the onions. Stir well and cook for another 2-3 minutes.
Pour in the pomegranate juice and stir well. Bring the mixture to a simmer.
Return the browned chicken pieces to the pot. Reduce the heat to low, cover, and let it simmer for about 1-1.5 hours, or until the chicken is cooked through and the sauce has thickened to a rich, gravy-like consistency. Stir occasionally and check for seasoning, adjusting salt, pepper, and sugar as needed.
If the sauce is too tart, add sugar to balance the flavor. If desired, add a tablespoon or two of lemon juice for extra tanginess.
Enjoy your meal!