Although quantum mechanics (QM) and quantum field theory (QFT) are highly successful, the seemingly simplest state -- vacuum -- remains mysterious. While the LHC experiments are expected to clarify basic questions on the structure of QFT vacuum, much can still be done at lower energies as well. For instance, experiments like PVLAS try to reach extremely high sensitivities, in their attempt to observe the effects of the interaction of visible or near-visible photons with intense magnetic fields -- a process which becomes possible in quantum electrodynamics (QED) thanks to the vacuum fluctuations of the electronic field, and which is akin to photon-photon scattering. PVLAS is now close to data-taking and if it reaches the required sensitivity, it could provide important information on QED vacuum. PVLAS and other similar experiments face great challenges as they try to measure an extremely minute effect. However, raising the photon energy greatly increases the photon-photon cross-section, and gamma rays could help extract much more information from the observed light-light scattering. Here we discuss an experimental design to measure photon-photon scattering close to the peak of the photon-photon cross-section, that could fit in the proposed construction of an FEL facility at the Cabibbo Lab near Frascati (Rome, Italy).