I once turned a vase/hollow form thing from a log of cork oak I lifted from a roadside in Portugal [I think]. The differing density between the wood and its thick cork coating made life extremely interesting. Cant for the life of me remember the exact method but I did succeed so it can be done. I seem to remember that the cork shrank away from the wood slightly, leaving a small step, but it wasn't enough to ruin the finished article, which kicked around here as a novelty for years.
Brian