Turning a plate on a lathe is a challenge because of the difficulty in holding the relatively thin piece of wood.  However, the task has been made much easier in recent years with a 4-jaw, self centering chuck that can grip either in expansion mode inside a turned, shallow void on the bottom, or contraction mode around a turned ring on the bottom.  (Click on any image to enlarge)

Teak is a naturally oily wood.  For a plate on which food will be served, and which is then going to go into soapy water, the natural oil helps preserve the wood and keep it from drying and cracking.