Bromoil printing doesn't involve any inkjet printing: you're the printer yourself! It is a very old printing process, wherein the silver in the image is replaced by ink. The Bromoil printing process was invented in 1907 be Englishman C. Welbourne Piper on a suggestion from E.J. Wall.
In short: print an image (conventional B&W print on a fibre based bromide paper from a negative), bleach, keep paper wet while stamping ink (any colour(s) you choose) on it with a special brush.
See: Making a Bromoil print for a better description.
It's one of my favorite alt-photo processes.