Love the term “Garden Folly.” Outbuilding or shed just doesn’t have the same caché.
To be fair to the name, in architecture, a true Folly is primarily (some might even say, strictly) for decoration. A true Folly doesn’t serve any other purpose. Obviously, a garden shed or outbuilding would be at least somewhat utilitarian. That doesn’t mean that your shed can’t have charm, beauty or an element of mystery.
Here are a few other images for inspiration:
Charlotte Moss in New York, one of my (and all of blogdom’s) all-time favorites: