In an article appearing in Physical Review Letters, Joseph Maciejko and collaborators from Stanford University, in collaboration with SLAC, Microsoft Research, and the University of Maryland, all in the US, propose an optical experiment to measure this. The setup consists of a layer of a generic topological insulator deposited on an ordinary insulator, in a perpendicular external magnetic field. They find that measuring the rotation of light polarization reflected off the top surface (Kerr angle) and transmitted through the two layers (Faraday angle) allows one to extract the quantized magnetoelectric response. If this measurement could be realized, topological phenomena in condensed matter physics could be used to nail down the most precise values for three basic physical constants: the fundamental electric charge e, Planck’s constant h, and the speed of light c.
This should rest all arguments that condensed matter physics is merely "applied physics" and has nothing fundamental.
Note that you get free access to the paper using that link.