We show that large aspect-ratio Vertical External-Cavity Surface-Emitting Lasers (VECSELs) with a saturable absorber can be operated in the regime of spatio-temporal mode locking. The emitted pulses exhibit a spatial profile resulting from the phase locking between an axial plane-wave with a set of tilted waves having a hexagonal arrangement in the Fourier space. We show that these pulsating patterns are temporally localized, i.e. they can be individually addressed by modulating the optical pump.The theoretical analysis shows that the emergence of these pulsating patterns is a signature of a Turing instability whose critical wave vector depends on spherical aberrations of the optical elements. Our result reveals that large aspect-ratio VECSELs offer unique opportunities for studying fully developed spatio-temporal dynamics.