In a small pan over medium heat, bring 1/2 cup maple syrup to a boil. Reduce heat and simmer until reduced by half, about 12 minutes. Cool slightly. In a bowl, combine butter, 1/2 tsp. salt, 1/2 tsp. pepper and chopped sage and thyme. Stir in reduced syrup. Place in refrigerator to cool, stirring frequently.
Preheat oven to 350ºF. Remove giblets and neck from turkey. Rinse turkey inside and out with cool water; pat dry. Gently loosen skin from breast. Spread 2/3 of butter mixture under skin. Season inside of turkey generously with salt and pepper and stuff with 8 onion wedges, garlic and herb sprigs. Tie drumsticks together and tuck wings under. Scatter remaining onion wedges in a large roasting pan, top with a rack and place turkey on rack. Spread remaining butter mixture all over turkey. Pour 1 cup of broth and 1 cup of apple cider into bottom of roasting pan. Cover loosely with foil. Roast turkey, basting every 30 minutes, until an instant-read thermometer placed in thickest part of thigh reads 165ºF, about 3 hours.
In the last half hour, remove foil and baste with half of reserved 1/3 cup maple syrup. Roast 15 minutes; repeat basting. Transfer turkey to platter, tent with foil and let rest for 20 to 30 minutes.
Make gravy: Remove rack from roasting pan and pour drippings into a measuring cup, leaving onion in pan. Skim fat from drippings and return 4 Tbsp. fat to pan. Place pan over 2 burners on medium heat. Sprinkle with flour and cook, stirring, for 3 minutes. Add remaining 2 cups of cider and 1 cup of broth and reserved drippings to pan. Bring to a boil, scraping up browned bits from bottom of pan, reduce heat to low and simmer until slightly thickened, about 10 minutes. Strain into saucepan and season with salt and pepper. Serve with turkey.