Preheat the oven to 325 degrees F.
Rub the turkey all over with the butter, including the cavity of the breast. Season generously with salt and pepper. Scatter the vegetables on the bottom of a roasting pan just large enough to hold the turkey. Set the turkey breast-side up in the pan. Roast until an instant-read thermometer inserted into the thickest part of the roast registers 160 degrees F, 2 to 2 ½ hours.
Transfer the turkey to a cutting board and tent loosely with foil for 30 minutes. (The breast temperature will continue to rise to 170 degrees F as it rests.)
Pour any pan drippings into a fat separator or small bowl. Reserve 3 tablespoons of the fat; discard the rest or the fat. Add the pan juices to the broth. Add the reserved fat to the roasting pan and place on a burner over medium-high heat. Scrape up any browned bits from the bottom of the pan with a wooden spoon. Stir in the flour and cook for 2 minutes, stirring constantly. Whisk in the broth and continue to stir. Bring to a boil and cook until thickened, about 3 minutes. Strain the gravy, discarding the vegetables, and season with salt and pepper to taste.
Carve the breast and serve with the gravy.
