I of course use wild turkey wings, but store-bought wings will work every bit as well; they won't take as long to braise though. I leave the choice of smoke and barbecue sauce up to you, but I used hickory wood and my bourbon BBQ sauce in this case. Remember these are addicting, so either have lots of wings -- or don't invite people over.
Salt the wings well and set them in a pot with a lid. Cover with water by 1 inch and bring to a strong simmer. Skim off any froth that forms on the surface of the water. Drop the heat to low and add salt to taste.
Add the herbs, onion, carrot and celery and simmer very gently until the wings are tender, anything from 90 minutes for store-bought birds and young jakes to 3 hours or more for gobblers. They will get tender, just give them time.
When the meat is tender but not yet falling off the bone, remove the wings. Let them cool just enough to handle, and then coat with the BBQ sauce of your choice. You can let them sit as little as 30 minutes or up to a day.
Get your grill or smoker ready, and when it's about 200°F and smoky, coat the wings with more BBQ sauce and set them in the smoker. Let them smoke as little as 30 minutes and as long as 3 hours; I prefer 90 minutes. After 1 hour has elapsed, paint the wings with more BBQ sauce.
When you're ready to eat them, you can either paint one more time with BBQ sauce or just eat them. Smoked turkey wings are good cold the next day, too.
You can strain and save the braising liquid, which is now a nice turkey broth. Use it for turkey risotto or soup.