Toasties on John Street makes it (Thanksgiving sandwich), but it's made from boneless turkey roast, not whole turkey. Also, it's one of the few places I'd accuse of using too little salt in their cooking.
Lenny's Gourmet Deli on Columbus between 83rd-84th. Fantastic. Great stuffing, freshly roasted turkey, gravy and cranberry sauce. They now have other locations throughout NYC but I can't vouch for those.