Using a food processor, crush the walnuts to form fine crumbs. Make sure not to overprocess, you don't want the walnuts to release their oil.
Heat 2 tablespoons of olive oil in a pot over medium high heat. Season the chicken with the turmeric, 1 teaspoon kosher salt and 1/2 teaspoon black pepper.
Sear the chicken for 5 minutes on each side. Remove the chicken and set it aside.
Heat the remaining olive oil in the pot and saute the onion until golden.
Add the walnuts and sauté for 5-10 minutes so they start releasing their aroma.
Add 6 cups of water. Turn the heat up to medium high and bring the mixture to boil, turn the heat down to medium and let it simmer for 1 hour, stirring occasionally.
Add the pumpkin, pomegranate molasses, salt and pepper and let it cook for 1 more hour.
Add the chicken back to the pot and simmer for another 30 minutes or until the chicken is fully cooked and the sauce has thickened.
Taste the stew and add more salt if needed, if it's not sour enough, add some more pomegranate molasses and if it's too sour, add 1-2 tbsp brown sugar.