I have a wood smoker, and I smoke raw eggs in it. I put them at the opposite end of the fire box, and let them stay for about 2 hours. More or less depending on the temp. The shells will turn a dark golden brown (if you start with white eggs) by the time they're done.
A little of the smoke makes it thru the shell on the eggs. We make deviled, salad, pickled, or just peel and eat.
I've been doing this for years, it's always a crowd pleaser, and people seem to like whatever it is that we make from these smoked eggs.