I turn lots of them on the lathe from both solid wood and glued-up blocks. I can turn almost 20" diameter boxes on my lathe... most home shop lathes are limited to 12" or so.

Framing in square frames is easy and lots of frames are available, though most are pretty cheesy. If your wood working skills can get you to a good tight miter joint you should be able to make a deeper frame... I have done some huge displays that way, but prefer the smaller round ones these days.

Do not have time right now to show the process, but I will soon. I know I have some decent pictures...
art