Freeze desalination involves cooling brine down to low temperatures using vapor compression cycle. For the feasibility of the freeze desalination technology, cold energy recovery from generated ice is indispensable which can be performed in numerous ways by adopting different configurations for the system. Identifying the optimum freeze desalination configuration is a key research gap that needs to be bridged for the technology to be feasibly utilized. This paper identifies the optimum freeze desalination configuration as well as the most energy-efficient operational parameters. A co-simulation framework has been developed coupling software tools ASPEN PLUS (handling brine's thermo-chemical properties) with MATLAB (simulating vapor compression cycle and orchestrating the data flow for the framework). The results show the work consumption profiles for the investigated system configurations and specify the optimum configuration as well as the most energy-efficient operational parameters related to the optimum configuration. The results have been validated against the benchmark published values of the least work of separation for desalination. The generated results present a reference for the design and operation of the freeze desalination system and process.