Preheat oven to 325°.
To prepare garlic-herb rub, place first 5 ingredients in a food processor; process until finely minced.
To prepare turkey, remove white papery skin from garlic head (do not peel or separate the cloves). Wrap garlic head in foil. Set aside.
Remove and discard giblets and neck from turkey. Rinse turkey with cold water; pat dry. Trim excess fat. Starting at neck cavity, loosen skin from breast and drumsticks by inserting fingers, gently pushing between skin and meat. Spread garlic-herb rub under loosened skin and rub over breast and drumsticks. Gently press skin to secure. Lift wing tips up and over back; tuck under turkey.
Place turkey on a broiler pan coated with cooking spray. Insert a meat thermometer into meaty part of a thigh, making sure not to touch bone. Bake at 325° for 1 hour. Add garlic head to pan; bake an additional 2 hours or until thermometer registers 180°. Place turkey on a platter, reserving pan drippings; let stand 20 minutes. Discard skin.
To prepare gravy, place a zip-top plastic bag inside a 4-cup glass measure. Pour pan drippings into bag; let stand 10 minutes (fat will rise to the top). Seal bag; carefully snip off 1 bottom corner of bag. Drain drippings into glass measure, stopping before fat layer reaches opening (you should have about 2/3 cup). Reserve 1 tablespoon fat; discard remaining fat. Add enough broth to drippings to measure 3 cups; reserve remaining broth for another use.
Separate roasted garlic cloves; squeeze to extract garlic pulp. Discard skins. Heat reserved fat in a medium saucepan over medium heat. Add garlic pulp and flour; cook 30 seconds or until lightly browned, whisking constantly. Gradually add broth mixture, stirring with a whisk until blended. Bring to a boil over high heat, stirring constantly. Remove from heat.