Using a sharp knife or pair of kitchen shears, remove the backbone of the turkey and set it aside for homemade turkey stock.
With the turkey breast side down, make an incision in the back of the breast bone.
Flip the turkey so that it is breast side up and press down on the breasts to flatten it.
In a container large enough to hold the turkey (I recommend a clean 5 gallon bucket), place 1 gallon of water, salt, sugar, crushed rosemary, dried sage, thyme, and savory. Stir to combine well.
Place turkey into the brine, add ice, and top off with additional water.
Place the bucket into the refrigerator and brine for 8 hours or overnight.
After the turkey has brined, remove it from brine, and pat dry. Discard brine.
Lay the turkey, breast side up, on a wire rack.
Gently seperate the skin and the meat of the breast, and the thighs.
Prepare the turkey compound butter by combining softened butter, parsley, rosemary, sage, lemon juice, and lemon zest. Stir to blend well.
Place the turkey on the wire rack over a pan large enough to accommodate the wire rack, I recommend a 4-inch-deep roasting dish. Doing this preserves the juices from the turkey you can use to make gravy.
Use your hands to gently push the compound butter between the breast meat and the skin. Work the compound butter under the skin. This will help baste the turkey while it cooks.
Heat the electric smoker to 225°F.
Place turkey in the roasting dish into the smoker.
Insert the temperature probe into the thickest part of the the breast.
Close the smoker lid and cook until it reaches an internal temperature of 100°F to 110°F, about 2 to 2½ hours.
Once the turkey has reached 100°F, raise the smoker temperature to 375°F.
Cook the turkey and baste with any of the rendered juices until the breast internal temp reaches 160°F. This should take between 1 and 1½ hours.
Remove the turkey from the smoker.
Place a foil tent over the turkey and allow the bird to rest for about 20 minutes before carving.