We observe an enormous spontaneous exchange bias (similar to 300-600 Oe)-measured in an unmagnetized state following zero-field cooling-in a nanocomposite of BiFeO3 (similar to 94%)-Bi2Fe4O9 (similar to 6%) over a temperature range 5-300 K. Depending on the path followed in tracing the hysteresis loop-positive (p) or negative (n)-as well as the maximum field applied, the exchange bias (H-E) varies significantly with vertical bar - H-Ep vertical bar > vertical bar H-En vertical bar. The temperature dependence of H-E is nonmonotonic. It increases, initially, till similar to 150 K and then decreases as the blocking temperature T-B is approached. All these rich features appear to be originating from the spontaneous symmetry breaking and consequent onset of unidirectional anisotropy driven by "superinteraction bias coupling'' between the ferromagnetic core of Bi2Fe4O9 (of average size similar to 19 nm) and the canted antiferromagnetic structure of BiFeO3 (of average size similar to 112 nm) via superspin glass moments at the shell. DOI: 10.1103/PhysRevLett.110.107201