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Phase transitions and the associated symmetry breaking are at the heart of many physical phenomena. Coupled systems with multiple interacting degrees of freedom provide a fertile ground for emergent dynamics that is otherwise inaccessible in their solitary counterparts. Here we show that coupled nonlinear optical resonators can undergo self-organization in their spectrum leading to a first-order phase transition. We experimentally demonstrate such a spectral phase transition in time-multiplexed coupled optical parametric oscillators. We switch the nature of mutual coupling from dispersive to dissipative and access distinct spectral regimes of the parametric oscillator dimer. We observe abrupt spectral discontinuity at the first-order transition point which can pave the way for the realization of novel transition-edge sensors. Furthermore, we show how non-equilibrium phase transitions can lead to enhanced sensing, where the applied perturbation is not resolvable by the underlying linear system. Our results can pave the way for sensing using nonlinear driven-dissipative systems leading to performance enhancements without sacrificing sensitivity.