For the turkey: Pat the turkey dry, inside and out. Place the onion and orange quarters into the cavity, tie the drumsticks together and tuck the wings under the bird.
Rub butter all over the skin, then sprinkle generously with salt and pepper. Place the turkey on a rack set over a roasting pan. Roast for 25 minutes.
Meanwhile, bring the orange juice and maple syrup to a boil in a small saucepan. Remove from the heat.
After 25 minutes, turn down the oven to 375 degrees F and glaze the turkey with the orange-maple mixture. Continue to roast, glazing the turkey every 25 minutes, until a meat thermometer inserted into the thickest part of the thigh reads 165 degrees F, 3 to 4 hours more, depending on the oven. Let rest for 15 minutes.
For the gravy: Meanwhile, Heat the olive oil and butter in a thick-bottomed saucepan or Dutch oven over medium-high heat. Add the shallots and thyme, and cook until brown. Add the flour; cook for 1 minute.
While whisking, slowly add the turkey drippings. Bring to a boil and cook, whisking, until thickened, 5 minutes. Taste and season with salt and pepper if needed.