1. Preheat the oven to 325 degrees.
2. In a medium Dutch oven, heat the oil and butter over medium-high heat. Season the turkey all over with salt and pepper and add to the pot. Brown the turkey on all sides, about 8 minutes total, and set on a plate.
3. Add the onions to the pot and cook, stirring frequently, until softened, about 3 minutes. Add the garlic and cook for 30 seconds. Add the chicken broth, orange juice and rosemary and bring to a boil. Return the turkey to the pot, cover, and bake in the oven for 30 minutes.
4. Stir the squash into the pot, coating it well with all the juices. Cover and continue to bake until an instant-read thermometer inserted into the center of the turkey reads 160 degrees, another 30 to 45 minutes.
5. Set the turkey on a carving board and tent loosely with foil. Using a slotted spoon, transfer the squash to a bowl and cover with foil.
6. In a small bowl, stir together the cornstarch and 1 tablespoon cold water until the cornstarch is dissolved. Add to the Dutch oven and bring the gravy to a boil over medium-high heat, stirring, until thickened, 1 to 2 minutes. Season the gravy with salt and pepper.
7. Slice the turkey and place on a serving platter with the squash alongside. Pass the gravy in a sauceboat at the table.
Sometimes I swap out the rosemary in this dish for sage. Turkey and sage is a classic pairing that works well with the earthy butternut squash.