Jason,
The easiest way to do it is to use a flexible veneer. It is generally 1/64 to 1/32 thick wood bound to a backing (sometimes laminated with foil). It is available in large sheets, applies with contact cement, finishes like normal thickness wood, and avoids all of the structural problems (cracking, warping, etc.) of a solid piece. The best logs in most species are used for veneer, and larger pieces of many wood are only available in veneer (i.e. carpathian elm burl, walnut burl, etc.).
Constantines supplies flexible and solid veneers in the rarest woods on earth. I have used then for 30+ years and never been disappointed.
http://www.constantines.com
If you need any help, I've done a fair amount of veenering - both solid and flexible. Just send an e-mail. It is a very easy process.