At least in the non-food printers, it's printed in color. They use dyes mixed into the binder and print it out exactly like an inkjet printer does.

That art looks next to impossible to paint onto the printed piece. Seems plausible that it could be done during printing. Some of these are really beautiful...

Looks like they lay down a thin layer of sugar and bind it with an inkjet head. So they can print layer by layer in full color.