Emulsions are omnipresent in the food industry, health care, and chemical synthesis. In this Letter the dynamics of metastable oil-water emulsions in highly turbulent (1011≤Ta≤3×1013) Taylor-Couette flow, far from equilibrium, is investigated. By varying the oil-in-water void fraction, catastrophic phase inversion between oil-in-water and water-in-oil emulsions can be triggered, changing the morphology, including droplet sizes, and rheological properties of the mixture, dramatically. The manifestation of these different states is exemplified by combining global torque measurements and local in situ laser induced fluorescence microscopy imaging. Despite the turbulent state of the flow and the dynamic equilibrium of the oil-water mixture, the global torque response of the system is found to be as if the fluid were Newtonian, and the effective viscosity of the mixture was found to be several times bigger or smaller than either of its constituents.