Prepare the rice as directed on its package. Strain any leftover liquid and put it aside (you'll end up with roughly 3 cooked cups).
Position an oven rack in the middle and heat the oven to 425°F (220°C). For simpler clean-up, line a 9×13-inch baking dish with a big sheet of aluminum foil or parchment. Set the chicken thighs in a single layer, folding the loose flap under each piece. Coat with 2 tablespoons of the oil and season with ¼ teaspoon salt and ¼ teaspoon pepper. Roast on the center rack until an instant-read thermometer registers 165°F (75°C) at the thickest part, about 20 minutes. Move the chicken right away to a plate and cover loosely. Allow to rest for 10 minutes. Lower the oven to 350°F (175°C). Dispose of the foil or paper but keep the dish close by.
While the chicken is roasting, peel the butternut squash and slice off both ends. Separate the neck from the bulbous base. Stand the base on a flat end and halve it vertically. Remove the seeds and throw them away. Dice both the neck and base into ½-inch cubes (you should get about 4 cups).
Warm the remaining 2 tablespoons of oil in a large, deep skillet that has a tight lid, over medium heat. Put in the squash, onion, plus the rest of the salt and pepper. Sauté for about 2 minutes until the onion starts to turn translucent. Cover and cook, stirring from time to time, until the squash is soft but still has a bit of bite, which takes 6 to 8 minutes.
After the chicken has rested, chop it into bite-size chunks. Add it to the skillet along with the thyme, cranberries, ¼ cup of Parmesan, and the cooked rice. Mix everything well.
Spray the same 9×13-inch baking dish with nonstick cooking spray (no need to wash it first). Use a large spoon to transfer the squash-rice mixture into the dish, smoothing it out evenly.
Bake for 15 minutes. Take the casserole out, then scatter the nuts and the remaining ¼ cup of Parmesan on top. Continue baking for another 8 to 10 minutes until the cheese melts and the nuts become toasted and crunchy. Finish with a sprinkle of extra fresh thyme and serve hot.