We report on the self-propulsion of boiling droplets which, despite their contact with viscous, immiscible oil films, attain high velocities comparable to those of levitating Leidenfrost droplets. Experiments and model reveal that droplet propulsion originates from a coupling between seemingly disparate short and long timescale phenomena due to microsecond fluctuations induced by boiling events at the droplet-oil interface. This interplay of phenomena leads to continuous asymmetric vapor release and momentum transfer for high droplet velocities.