We demonstrate a new guiding regime termed endlessly mono-radial, in the proposed annular core photonic crystal fiber (AC-PCF), whereby only modes of the fundamental radial order are supported by the fiber at all input wavelengths. This attribute is of high interest for applications that require the stable and broadband guiding of mono-radial (i.e. doughnut shaped) cylindrical vector beams and vortex beams carrying orbital angular momentum. We further show that one can significantly tailor the chromatic dispersion and optical nonlinearities of the waveguide through proper optimization of the photonic crystal microstructured cladding. The analytical investigation of the remarkable modal properties of the AC-PCF is validated by full-vector simulations. As an example, we performed simulations of the nonlinear fiber propagation of short femtosecond pulses at 835 nm center wavelength and kilowatt-level peak power, which indicate that the AC-PCF represents a promising avenue to investigate the supercontinuum generation of optical vortex light. The proposed fiber design has potential applications in space-division multiplexing, optical sensing and super-resolution microscopy.