Naturally available optical materials are known to provide a wide variety of electric responses, spanning from positive to negative permittivity values. In contrast, owing to drastically modified conduction properties at the microscopic level, at such high frequencies magnetism and conductivity are very challenging to realize. This implies that extreme (high or low) values of permittivity, although highly desirable for a wide range of optical applications, are difficult to realize in practice. Here, we suggest the design of an engineered resonant nanoparticle composed of two conjoined hemispheres, whose optical response may be changed at will from an ideal electric conductor to an ideal magnetic conductor. Near the nanoparticle internal resonant frequency, we derive a closed-form solution that describes the electromagnetic response of this nanoparticle, showing how its light interaction may become dramatically dependent on the local field polarization, passing through all possible impedance values (from zero to infinity) by a simple mechanical or polarization rotation. Considering realistic frequency dispersion and loss in optical materials, we further show that these concepts may be applied to different geometries, with possibility for future experimental feasibility. We forecast various applications of this geometry as an optical nanoswitch, a novel nanocircuit element and as a building block for novel optical metamaterials.