A slit in a thick metal plate that is extremely subwavelength will not transmit microwaves polarized parallel to it. It is shown here that cuts perpendicular to the slit allow parallel polarized radiation to resonantly transmit. Furthermore, a zero-order mode may be excited within the slit, the frequency of which, to first order, is independent of the plate depth. Remarkably, for this novel type of resonance, the field in the slit oscillates with a constant phase and little amplitude variation throughout the plate depth, while the resonant wavelength tends to infinity as the slit width approaches zero.