Tom Colicchio's Herb-Butter Turkey

INGREDIENTS

• 2 teaspoons minced fresh rosemary plus 5 fresh rosemary sprigs
• 2 teaspoons minced fresh thyme plus 15 fresh thyme sprigs
• 1 cup diced celery
• 2 tablespoons (1/4 stick) unsalted butter
• 1 cup (2 sticks) butter, room temperature, divided
• 2 cups diced onions
• 6 cups (or more) low-salt chicken broth
• 2 pounds turkey necks and/or wings
• 2 teaspoons minced fresh tarragon plus 5 large fresh tarragon sprigs
• 1/4 cup all purpose flour
• 1 14- to 16-pound turkey
• 4 cups low-salt chicken broth, divided
• 1 cup diced peeled carrots
• 2 teaspoons minced fresh sage plus 5 fresh sage sprigs