Place the chicken pieces in a Dutch oven with 2 tablespoons of oil on medium-high heat. Sear the chicken on both sides until it becomes golden and crispy, 5 minutes on each side.
Remove from the pot and set it aside. You can leave the chicken fat in the pot or remove it. However, if you decide to discard the fat, you will need to add 2 more tablespoons of oil to sauté the onions in the next step.
Toss in the onions and saute for 10 minutes until lightly brown.
While the onions are cooking, in a food processor pulse the walnuts until finely ground. Don’t overdo it, otherwise, you will have walnut butter. Set aside.
Add the ground walnuts to the pan with onions and stir over medium heat for a couple of minutes.
Add the water, pomegranate molasses, salt, and pepper and stir to incorporate all the items into the pan.
Now return the chicken and any accumulated juice to the pan and press them down to fully immerse them into the sauce.
Cover, keep the flame on low, and simmer for 45 minutes. Take extra care and stir occasionally to prevent this thick stew from burning on the bottom.
Taste and make any necessary adjustments by adding more pomegranate molasses if needed. You're aiming for a robust pomegranate flavor with a balanced sweet and tart profile.
Continue to simmer for another 45-60 minutes. The stew should have turned into a deep maroon color and the chicken should be fork tender.
Add the saffron water, stir, and taste one more time and make any last minute adjustments by adding more sugar or lemon juice, if desired.
Remove from the heat and allow to sit for 10 minutes before serving.
Serve with steamed Persian saffron basmati rice.