Combine apricot nectar, preserves, ginger, and honey in a small saucepan and bring to boil. Reduce heat to medium-low, and simmer until thickened and reduced to 1-1/4 cups, about 15 minutes.
Blend 3/4 cup unsalted butter at room temperature, 3 tablespoons chopped fresh sage, salt, and pepper in small bowl. Set aside.
Melt 2 tablespoons unsalted butter in a large heavy skillet over medium heat. Add onions and shallots; saute until very soft and light brown, about 20 minutes.
Position rack in lowest third of oven. Preheat to 400 degrees F (200 degrees C).
Season turkey cavity with salt and pepper. Place turkey, breast side up, on a rack in a large roasting pan. Slide hand under skin of turkey breast to loosen skin. Spread half of herb butter over breast under skin. Rub remaining herb butter over outside of turkey.
If stuffing turkey, spoon stuffing loosely into main cavity; it will expand as it cooks. Tie legs together loosely to hold shape of turkey.
Roast turkey for 30 minutes in the preheated oven. Reduce oven temperature to 325 degrees F (165 degrees C), and continue roasting 1 hour 30 minutes, basting occasionally with pan drippings. Tent turkey with aluminum foil; roast 45 minutes longer.
Add onion mixture, 1 cup broth, thyme, and 1/2 teaspoon chopped fresh sage to the roasting pan. Roast 15 more minutes before brushing 1/2 cup apricot glaze over turkey. Continue to roast turkey uncovered, brushing occasionally with glaze. Add more broth to the pan if necessary. Bake 40 minutes longer for unstuffed turkey, and 1 hour 10 minutes longer for stuffed turkey, or until meat thermometer inserted into the thickest part of the thigh registers 165 degrees F (75 degrees C). Place turkey on a platter, and tent with foil. Let stand 30 minutes. Reserve mixture in pan for gravy.
Pour contents of roasting pan into a strainer set over a large bowl. Skim fat from pan juices using a large spoon. Transfer the onion mixture to a blender. Add 1 cup pan juices, and puree until smooth, adding more pan juices and chicken broth if necessary to thin sauce to desired consistency. Transfer sauce to a large saucepan, and bring to a boil. Cook until color deepens, skimming off any foam, about 5 minutes. Season with salt and pepper.