We present research program and project for high-resolution wavelength-dispersive spectrometer dedicated to low-energy X-ray spectroscopy at the electron cooler of the CRYRING@ESR storage ring, which is a part of the international Facility for Antiproton and Ion Research (FAIR) currently being built in Darmstadt. Due to the unique shape of the electorn-ion recombination X-ray source, resulting from the overlapping of the electron and ion beams in the electron cooler, the spectrometer can work in the specific asymmetric von Hamos (AvH) geometry. In order to completely eliminate the influence of Doppler effect on the measured X-ray energies, two asymmetric von Hamos spectrometers will be installed next to the dipole magnets on both sides of the electron cooler to detect blue/red (0°/180°) shifted X-rays, e.g. emitted in the radiative recombination (RR) process. The X-ray-tracing Monte-Carlo simulations show that the proposed AvH spectrometer will allow to determine with sub-meV precision, the low-energy X-rays (5–10 keV) emitted from stored bare or few-electron heavy ions interacting with cooling electrons. This experimental precision will enable accurate studies of the quantum electrodynamics (QED) effects in mid-Z H- and He-like ions.