After much discussion with DH, we agreed that Poor Man's Asparagus should be acceptable. Which means pacanis was the first to guess it. The one pictured is actually called Sea Asparagus. It's also called by many different names, glassworts, sea pickle, rock samphire, pickleweed.
Oh, I forgot to mention, it's in the Salicornia genus, the beet family.
It has been known to grow in marshes. It's one of the up and coming crops in Hawaii since it has a very high tolerance for salt. I've yet to try these locally and still waiting for a friend to bring some pickled ones back for me when she goes to visit her Mom on Oahu.
Whew, I see I got it. I was still looking for that exact pic, if it's out there, to see exactly what kind you were looking for.
Looks interesting and sounds like something I'd like to try.