Position oven rack in bottom third of oven and preheat to 350F. Place shallots, garlic and thyme sprigs in a small ovenproof baking dish and drizzle with olive oil. Cover dish with foil and bake until shallots are very tender but not brown, about one hour. Uncover and cool 30 minutes.
Place garlic, half of shallots and oil in work bowl of a food processor. Add chopped thyme, mustard, salt and pepper. Process until almost smooth. Transfer paste to a small bowl. Shallot paste can be covered with plastic wrap and refrigerated for up to four days.
Rinse turkey inside and out with cold running water and pat dry. Starting at the neck end, carefully slide your hand between the turkey's skin and breast to loosen skin. Spread a half cup of shallot paste under skin and over breast meat. Tuck wings underneath the body of the turkey and tie legs together loosely with kitchen twine or dental floss so the turkey will hold its shape. Place turkey on a small wire rack set inside a large roasting pan. Spread a half cup of shallot paste all over the outside of the turkey neck, gizzard and heart and place onion, celery and thyme sprigs in the pan around turkey.
Bring a cup of the wine and two cups of the broth to a boil in a medium saucepan. Pour boiling liquid into bottom of roasting pan. Cover breast loosely with foil and place turkey in oven. Roast for one and a half hours. Add a cup of the broth and a cup of wine to the pan and roast turkey another 30 minutes. Remove foil and add a cup broth to pan.
Continue roasting until an instant-read thermometer inserted in the thickest part of the thigh registers 175 degrees F, another one to one and a half hours. During roasting, cover exposed parts of turkey with foil as needed to prevent over-browning and add more broth if pan juices evaporate.
Remove turkey from oven and transfer to a platter. Tent turkey loosely with foil and let rest 30 minutes - its internal temperature will rise another 5-10 degrees. Reserving drippings and discard neck, gizzard and heart. Place turkey on a serving platter, carve and serve with gravy.