High resolution spectral observations of the polar EF Eridani obtained in a low state with X-Shooter revealed narrow emission lines from the irradiated secondary. The lines were most prominent in the near-IR Caii-triplet, the more intensive Hα line had additional emission likely originating from an accretion stream. The lines with a radial velocity amplitude, K 2 = 385 ± 4 km s −1 , serve as tracer of the otherwise unseen companion. The mass function implies a massive white dwarf with M wd > 0.65 M at 3σ confidence, and a short distance to the binary, d ∼ 111 pc (<145 pc at 3σ confidence). The spectral energy distribution from the UV to the IR together with the high mass ratio gives further strong evidence of EF Eri being a post period-minimum object with M 2 < 0.06 M .