We have succeeded in growing epitaxial and highly stoichiometric films of EuO on yttria-stabilized cubic zirconia (YSZ) (001). The use of the Eu-distillation process during the molecular beam epitaxy assisted growth enables the consistent achievement of stoichiometry. We have also succeeded in growing the films in a layer-by-layer fashion by fine tuning the Eu vs. oxygen deposition rates. The initial stages of growth involve the limited supply of oxygen from the YSZ substrate, but the EuO stoichiometry can still be well maintained. The films grown were sufficiently smooth so that the capping with a thin layer of aluminum was leak tight and enabled ex situ experiments free from trivalent Eu species. The findings were used to obtain recipes for better epitaxial growth of EuO on MgO (001). ; Comment: 10 pages, 15 figures