The day before roasting, rinse the turkey inside and out with cold water, set on a clean kitchen towel and pat dry. Sprinkle the turkey inside and out with the salt. Wrap the turkey in plastic wrap and refrigerate, about 24 hours.
Remove the turkey from the refrigerator 1 to 2 hours prior to roasting to bring to room temperature.
Place an oven rack on the lowest rung and preheat the oven to 425 degrees F.
Place a few sprigs of the oregano and thyme, a few cloves of the garlic and a quarter of the lemon in the turkey's neck cavity. Wrap the neck skin over and around the cavity to enclose the ingredients. Place half of the remaining oregano, half of the remaining thyme, half of the remaining garlic, 2 lemon quarters, half of the fennel, half of the onion and all the fennel fronds in the turkey's body cavity. Place the turkey, breast-side-up, on a rack set into a large roasting pan. Fold the wings and tuck the tips underneath the turkey.
Melt the butter in a saucepan over medium heat, and then let cool.
Fill a pot with the stock. Add the remaining oregano, thyme, garlic, 1 quarter lemon, fennel and onions to the pot. Bring the stock mixture to a boil, reduce the heat so that the liquid simmers and continue to cook at a low simmer, about 10 minutes. Remove the pot from the heat and allow to cool slightly.
Soak a double layer of cheesecloth big enough to cover the turkey in the cooled butter and drape over the breast and legs of the turkey. Pour the stock mixture over the bird, pushing the pieces of vegetable and herbs into the bottom of the roasting pan. Add the reserved neck and gizzards to the bottom of the roasting pan.
Place the turkey in the oven and roast, about 45 minutes. (There will be the distinct possibility of smoke depending on how clean your oven is). Turn the temperature down to 375 degrees F, and continue to roast until an instant-read thermometer inserted into the center of a thigh registers 160 degrees F, 15 to 20 minutes (removing the cheesecloth for the final 10 minutes to brown, if needed). Remove the turkey from the oven and allow to rest before carving, about 20 minutes.
Recipe courtesy of Michael Symon