If you were going to recommend a single book to a non-design thinking software developer to expose them to the relevance and importance of design, what would you recommend?

Donald Norman, "The Design of everyday things". It will forever change your perpective on things like door handles and vendor machines, and has the potential of making you start thinking in fundamentally new patterns to make usable software.

One of the most influential books I've ever read on the subject is Richard Coyne's http://mitpress.mit.edu/books/designing-information-technology-postmodern-age(it's a little "heavy" but a great overview of the philosophy of design). Another great book is Donald Pye's http://www.cambridge.org/ca/academic/subjects/arts-theatre-culture/architecture/nature-and-art-workmanship(it's oriented toward industrial design but still a pretty good read).

The Design of Everyday Things is also offered as MOOC on udacity. Link: https://www.udacity.com/course/viewer#!/c-design101/l-300766461/m-440158645