In a large bowl, toss the butternut squash with 2 tablespoons of oil and 1/2 teaspoon of salt. Spread the squash evenly on a baking sheet and roast for 25 minutes, until the edges begin to caramelize and the squash is just starting to become tender (but not fully cooked). Remove from the oven and set aside.
Heat a Dutch oven over medium-high heat and add the remaining 2 tablespoons of oil. Place the chicken pieces in the pot, skin side down, and sear for about 5 minutes. Flip the chicken and sear for another 5 minutes on the other side.
Remove the chicken and set it aside. In the same pot, add the onions and sauté for 5-7 minutes, until lightly caramelized. Stir in the turmeric and cook for another 2 minutes.
Return the chicken to the pot, pour in the water, and add the remaining 1 teaspoon of salt and the pepper. Bring the mixture to a gentle simmer. Once simmering, cover the pot, reduce the heat to low, and cook for 45 minutes.
After the chicken has cooked for 45 minutes, add the golden plums, cinnamon, sugar, lime juice, and saffron water. Stir, then carefully add the roasted squash, submerging the pieces in the sauce. Cover and cook for another 30 minutes. Adjust the liquid as necessary, keeping in mind that the stew should not be too watery at the end.
Transfer the stew to a serving bowl, taking care not to break up the squash pieces. Serve with Iranian saffron basmati rice.