When symmetry is broken in plasmonic nanostructures, new optical properties emerge. Here we controllably reshape an individual Au nanoshell into a reduced-symmetry nanoegg, then a semishell or nanocup by a novel electron-beam-induced ablation method, transforming its plasmonic properties. We follow the changes in the plasmonic response at the single nanostructure level throughout this reshaping process, observing the splitting of plasmon modes and the onset of electroinductive plasmons upon controlled, incremental opening of the outer metallic layer of the nanoparticle.