I suppose, for me, it'd be one of the decent lugged, relaxed-geometry MTB frames of the 1980's paired with a collection of quality "period" components.

A modern rendition: probably something like a V-O Piolet or Campeur frame, done up similarly.

Something like this: V-O Piolet @ BlueLug; or V-O Campeur @ Velo-Orange; or V-O touring bike @ Velo-Orange BLOG; or similar, with color-matching treatment like this Surly Cross Check.

In such a build, much of "the look" would come from a proper selection of parts that could emulate the classic approach Rivendell brings.