Most of broad hat is dark (6)
I believe the answer is:
sombre
'is dark' is the definition.
(I've seen this before)
I can't explain the rest of the clue.
(Other definitions for sombre that I've seen before include "Joyless" , "Grave or gloomy" , "Gloomy and dismal" , "Dark and gloomy of manner" , "Melancholy" .)