The Collaborative International Dictionary of English v.0.48:

Finnan haddie \Fin"nan had"die\ (f[i^]n"nan h[a^]d"d[i^]). [See
   Haddock.]
   Haddock cured in peat smoke, originally at Findon (pron.
   f[i^]n"an), Scotland. The name is also applied to other kinds
   of smoked haddock. [Written also finnan haddock.]
   [1913 Webster]

WordNet (r) 3.0 (2006):

finnan haddock
    n 1: haddock usually baked but sometimes broiled with lots of
         butter [syn: finnan haddie, finnan haddock, finnan,
         smoked haddock]