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It’s complicated because there is no single authoritative map. Many different people design and regularly publish Garmin-comptible maps using OSM data, in many different styles, with different features, covering different areas. You can read more about that process in muralito’s second link.

If you don’t have the time or inclination to research making your own, just look at muralito’s first link and find people who are publishing maps of Denmark. Download them and try them out. (You probably won’t find any maps covering only the Faroe Islands – though of course you can create your own.)

I’m not familiar with the Garmin 2567 but probably you’d just need to copy the downloaded map file to a SD card and put it in the GPS. It might need to be in a particular directory or named a particular way for the Garmin to see it. And it might require some messing around in the device settings before it will start using the new map. But this is a feature explicitly supported by Garmin, and Garmin’s documentation should describe the process.

Just out of curiosity – does Garmin’s included map on the 2567 neglect the Faroes?