Heat the oil in a large heavy skillet over medium heat. Stir in sliced onions; cook and stir until the onion has softened and turned translucent, about 5 minutes. Reduce heat to medium-low, and continue cooking and stirring until the onion is very tender and dark brown, 15 to 20 minutes more.

Raise heat to medium-high. Add chicken pieces, and fry until lightly browned on the outside. Pour in the water, and bring to a boil. Reduce heat to low and simmer for about 30 minutes, adding more water if necessary to keep the mixture from drying out.

Preheat the oven to 325 degrees F (65 degrees C).

Combine the walnuts and pomegranate juice in the container of a blender or food processor. Process into liquid. (This can be done in small batches if necessary.) Add walnut-pomegranate mixture to the simmering chicken. Season with cardamom, cinnamon, saffron powder, and salt. Stir in the cubed squash. Transfer the entire mixture to a 9x13-inch baking dish.

Bake, loosely covered, for 2 1/2 hours in the preheated oven. Serve with white rice.