This paper reports in detail on the image-based modelling and unwrapping approach used to create a two-dimensional projected map of an astonishing ostrich egg globe from AD 1504. This miniature egg globe is not only the oldest extant engraved globe, but it is also the oldest post-Columbian globe of the world and the first ever to depict Newfoundland and many other territories. The intention of digitally recording the surface geometry and colour of this unique artefact was to portray the original layout of the world map used by the Florentine Renaissance artist to make this globe. In addition, it was expected to substantiate iconographical details, which are hard to study at its scale of 1:80,000,000. The ostrich egg globe is the prototype of the Lenox Globe kept at the New York Public Library. The latter is very beneficial to examine how the egg globe looked like before being glued together at its equator. On the other hand, unfolding the map engraved in the ostrich egg halves enables a more detailed study of the remarkable details visible on both globes, since the engravings on the quasi-white egg surface are much easier to discern than those of the highly reflective red copper Lenox Globe. Finally, a detailed study of the unwrapped 3D surface is essential to learn more about the world vision of its creator and the incredible efforts that went into making this globe. Thanks to some particular pictographic details as well as the way in which the engravings are applied (by a left-handed person), the globe artist can be identified as Leonardo da Vinci.