If you buy a frozen bird, remember to allow at least 3 days for it to thaw in the refrigerator.
Remove giblets and neck from turkey; reserve for making homemade broth, if desired. Rinse turkey with cold water; pat dry. Sprinkle cavity with salt and pepper. Place turkey, breast side up, in a greased broiler pan.
Combine softened butter and 2 tablespoons chopped thyme, stirring well. Using fingers, carefully loosen skin from turkey at neck area, working down to breast and thigh area. Spread 1/4 cup butter mixture under skin.
Tie legs together with heavy string, or tuck them under flap of skin. Lift wingtips up and over back, and tuck under bird. Generously rub salt and pepper over turkey. Tent turkey loosely with aluminum foil; roast at 325° for 1 hour.
Melt remaining thyme butter in a small saucepan over low heat; set aside for basting.
Peel shallots and place in a bowl; drizzle with olive oil and sprinkle generously with salt and pepper. Set aside.
Uncover turkey; baste with several tablespoons melted thyme butter mixture. Roast 1 hour, basting occasionally with butter mixture. After second hour of roasting, scatter shallots in pan around turkey; baste turkey. Roast 1 more hour or until a meat thermometer inserted into meaty part of thigh registers 180°, basting turkey and shallots every 15 minutes with butter mixture and pan drippings.
When turkey is done, carefully transfer it to a serving platter; arrange shallots around turkey. Cover with foil, and let turkey rest 15 minutes before carving. Reserve drippings in pan for Last-Minute Gravy. Prepare gravy. Garnish platter just before serving, if desired.