Cut the melon into quarters and remove the seeds. Remove the flesh from the skin and cut into slices. Cut mozzarella into slices as well. Arrange melon, mozzarella and ham on a large plate. Season with pepper.
Wash the basil, remove the leaves. Mash them coarsely with salt and oil in a mortar (or mix everything briefly with a hand blender). Sprinkle basil paste over melon and mozzarella.