Competition among eighteenth and nineteenth century book binders spurred many on to ever more elaborate displays.* Printer/publishers tended to sell you folded sheets. You then took them to your binder to turn the sheets into a volume handsome enough to be included in your personal library. Edwards of Halifax, one of the best binders of the time, were known for the excellence of their fore-edge painting. (As you can see from The British Library database, they also did many translucent vellum bindings.)
The Lilly Library of Bloomington Indiana has a nice on-line exhibition showing examples of fore-edge painting from their holdings. The banner at the top appears to show John Gilpin well on his way to Ware.
Fore-edge painting was done in water color, usually on fanned-out pages so that the picture was actually carried on a narrow strip down the edge of each page. The book was often gilded afterwards, and that would make the illustration invisible until the pages were fanned again. There were double fore-edge painted books, showing different pictures if fanned from the front or fanned from the back. Apparently some virtuosos would do double fanned edge painting on top and bottom too, though the top and bottom ones must have been hard to fan.
Books with painted fore-edges can be found from the middle ages, but the full elaboration of the art really got going from the middle of the seventeenth century, remaining popular till the early nineteenth century. Antiquarians debate the authenticity of some volumes as the edge-painting was executed long after the book had been bound. This seems overly nice to me: surely either way it’s an amazing skill.
Unfortunately I can’t find any dating information on that gigantic Borghese account book, but I like to imagine its being early.
I doubt whether any modern book binding lines have been adapted with ink-jet printing equipment so as to incorporate such a feature. Probably it should remain a handcraft option: no doubt there’s still the odd book or two getting fore-edge painting on a one-off basis. If you are going to pay for a top class hand binding, why not go the whole hog?
ABAA (the Antiquarian Booksellers’ Association of America) has an article about the process, straightforwardly entitled A collector’s guide to fore-edge painting by Jeff Weber.
Here’s an article from Atlas Obscura with many examples.
* The Bind is a late manifestation of this elaboration.