Optical vortices have myriad applications in photonics. Very recently, promising concepts of spatiotemporal optical vortex (STOV) pulses based on the phase helicity in the space-time coordinates have attracted much attention owing to their donut shape. We elaborate on the molding of STOV under the transmission of femtosecond pulses through a thin epsilon-near-zero (ENZ) metamaterial slab based on a silver nanorod array in a dielectric host. At the heart of the proposed approach is the interference of the so-called main and additional optical waves enabled by strong optical nonlocality of these ENZ metamaterials, which leads to the appearance of phase singularities in transmission spectra. The cascaded metamaterial structure is proposed for high-order STOV generation.