1. Make turkey: In a small bowl, combine butter, thyme, parsley, 3/4 tsp. salt and 1/2 tsp. pepper.
2. Remove neck and giblets from turkey; discard. Rinse turkey inside and out with cool water and pat dry. Season cavity with salt and pepper. Halve 1 onion and place in cavity along with lemon halves and thyme sprigs. Starting at neck end, carefully slide your fingers between skin and breast meat to loosen skin. Reserve 1 Tbsp. of butter mixture. Spread half of remaining butter mixture over breast meat under skin. Tuck wings under; tie legs together loosely with kitchen twine.
3. Preheat oven to 350ºF. Slice remaining onion and sprinkle over bottom of large roasting pan. Place rack on top. Place turkey on rack, breast side up, and spread second half of butter mixture all over. Cover turkey with foil.
4. Pour broth into bottom of roasting pan. Roast turkey for 30 minutes. Carefully remove foil and baste bird all over. Replace foil and continue roasting for 1 1/2 hours, basting every 30 minutes. Remove foil from turkey and continue roasting, basting every 20 minutes, until turkey is golden brown and thermometer inserted into thickest part of thigh registers 180ºF, about 1 hour and 15 minutes longer. During final basting, brush remaining 1 Tbsp. butter mixture over breast.
5. Remove turkey to a platter, tent loosely with foil and let rest 20 minutes.
6. Make gravy: In a saucepan over low heat, cook cranberries and sugar, stirring, until sugar has dissolved and berries have burst, about 10 minutes. Transfer to a blender and puree until smooth.
7. Remove onions from roasting pan with a slotted spoon and pour juices into a bowl. Skim off fatty liquid from top, reserving 3 Tbsp. Add enough broth to pan juices to make 5 cups liquid. Return reserved fatty liquid to roasting pan, add butter and allow to melt. Sprinkle flour on top and cook on stove over 2 burners set to medium heat, whisking, for 2 or 3 minutes. Pour in broth and cranberry mixtures and bring to a boil, whisking constantly. Reduce heat; simmer for 15 minutes. Strain into saucepan and season with salt and pepper.
8. Carve turkey and place on a platter. Pass gravy on the side.