A few PCB manufactures do full color PCBs now(Both JLC and PCBWay do, probably others too)
As of september year they had different processes for ordering, not sure if it's changed at all for either of them since then
JLC you had to use their EasyEDA Pro software to design the PCB(or import a project from another EDA and double check your work to make sure it didn't mess anything up) and import the image for the silkscreen, and export it a certain way
PCBWay you submitted the gerber files in the regular way, and then send them the image of what you want on the board.
(example courtesy of
@GutBomb , EricSCSI)
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