In a large bowl, Tupperware, or plastic zip-close bags (whatever you choose to marinate the chicken in), combine the tahini marinade and chicken parts. Rub marinade all over chicken and under the skin. Cover and refrigerate for at least 2 hours, up to overnight.
When ready to cook. Let the chicken come to room temperature. Position a rack in the middle of the oven (If doubling the recipe, position a rack in the upper third of the oven as well). Preheat to 400°F. Line a sheet-pan with parchment-paper.
Place carrots and shallots onto parchment-lined sheet-pan and toss to combine with half the avocado oil, half the garlic powder, a big sprinkle of kosher salt, and freshly ground black pepper. Spread out evenly on the sheet pan and then place chicken pieces into the empty spaces on the pan within the vegetables.
Roast for 20 minutes. Meanwhile, in a medium bowl, combine the butternut squash with the remaining avocado oil, the remaining garlic powder, a big sprinkle of Kosher salt, and freshly ground black pepper. Add the squash to the pan after everything has roasted for 20 minutes. Scatter lemon slices throughout the vegetables. Return to the oven and cook for another 35-40 minutes, until the vegetables are tender and chicken is cooked through and skin is crispy (TIP: If skin isn’t looking crispy in the last 10 minutes, move sheet pan to the top rack).
At this point your chicken is ready to eat with the vegetables and delicious drippings. However, if you’d like to go a step further, pour the juices from the bottom of the pan into a small saucepot and bring to a boil over medium-high heat. Cook until slightly thickened and reduced, then pour into serving dish with the vegetables and serve with the chicken.
Sprinkle roasted pistachios over entire dish and serve with Zhoug on the side, to drizzle over the chicken and vegetables, as desired.