Options for mounting a ceiling fan box directly to interior wooden Ridge Beam
Routing into the beam is probably not a practical option, you can't notch the bottom of the center of a beam without compromising it structurally.  

I would use a surface raceway, wiremold is popular but there are others.  Wiremold makes a Solid Base Fan Box Fitting that will make things very straightforward, the instructions illustrate things very clearly.  

If the customer doesn't like the appearance of a surface raceway, it's always possible to strip off the drywall, surface mount conduit, then rebox around the beam and conduit - but in most cases, the expense of that work will make the surface raceway seem a lot prettier.