In classical electrodynamics, light waves propagating in vacuum do not interact. In quantum physics, however, photon-photon interactions are mediated by virtual particles, giving rise to the electromagnetic nonlinearity of vacuum (EMNV). A direct measurement of EMNV would test a long-standing prediction of quantum electrodynamics and constrain new physics models. Despite its fundamental significance and extensive efforts to detect it, free-space EMNV has not yet been directly measured in the laboratory. Here, we propose a tabletop all-optical measurement of EMNV based on resonantly enhanced four-wave mixing in focusing optical resonators with a circulating power of a few megawatts. As a key experimental step toward this measurement, we demonstrate a resonator reaching a circulating power of 2.5 MW, approaching the parameter range needed to detect EMNV at the level predicted by quantum electrodynamics.