Guy at the LFS said it is "Sort of like a Brain Coral". I should have pushed him to be specific, but didn't. I really love this guy, but want to know exactly what I am dealing with.
may need to see the skeleton part for better identification. However, these guys are temperamental, so don't just go picking it up and flipping it around.
I'm going with acanthophyllia (meat coral). I am not inclined to touch him - he looks quite happy right where he is. Here is pic after 24 hours. Looks great!