Preheat oven to 450°. Line a large rimmed baking sheet with foil.
Place shallot, onion, and garlic in an even layer on prepared pan.
In a small bowl, stir together butter, oregano, 3 teaspoons salt, rosemary, thyme, and pepper. Spread butter mixture over turkey. Place turkey on pan, skin side up. Arrange herb sprigs around turkey.
Bake for 30 minutes. Reduce oven temperature to 325°. Baste turkey with pan juices, and bake until golden brown and a meat thermometer inserted in thickest portion registers 165° for breast pieces, and 170° for thighs, wings, and drumsticks, about 15 minutes more. Cover with foil, and let rest for 20 minutes. Discard herb sprigs.
Strain pan drippings, reserving ⅔ cup. Remove garlic from skins; using the back of a spoon, mash into a smooth paste.
In a small saucepan, whisk together reserved ⅔ cup drippings and flour. Cook over medium heat for 3 minutes, whisking constantly. Add broth and garlic paste; cook, whisking occasionally, until thickened, about 15 minutes. Stir in remaining ¼ teaspoon salt. Serve turkey with gravy and onions. Garnish with oregano, rosemary, and thyme, if desired.
Notes
If cooking both breasts and thighs, they should reach their respective temperatures around the same time.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/sheet-pan-turkey/