You just described how a commercial ice machine works. Cycle starts, and a valve fills up a tank to a preset level. A pump recirculates the water over the evaporator / mold. A probe senses the ice thickness and advances the cycle once the desired thickness is achieved. The refrigeration loop is then switched to "hot gas defrost", where the metering device is bypassed. Hot compressor gas goes through the mold, and the ice falls out. After a short time, the cycle starts over.
These commercial ice makers are a whole lot more efficient at making ice than a home refrigerator ice maker. For a 6000 btu machine, it's typically able to make 500 pounds of ice per day. That's a lotta ice!
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