High-energy, multi-octave supercontinuum (SC) generation in bulk media pumped with picosecond pulses in the mid-infrared, though pivotal in a myriad of applications, poses severe constraints due to wavelength scaling of the critical power criterion and the propensity to induce avalanche-ionization-seeded breakdown mechanisms. Here, we demonstrate a simple experimental geometry, relying on a very low numerical aperture for the pump pulse, and a crystal length commensurate with the Rayleigh length of the focusing geometry, generating a multi-octave, stable SC in yttrium aluminum garnet (YAG). The SC ranges from 500~nm to 3.5~μm (measured at -30  dB with spectral components at wavelengths up to 4.5~μm) when pumped by a 3~ps pulse centered at 2.05~μm in the anomalous dispersion regime. We also investigate the dynamics of filament formation in this interaction regime by monitoring the spectral and temporal evolution of the pulse during its propagation through the length of the crystal.