A method and machine for making frozen custard or similar products includes a freezing barrel, a pump for providing liquid mix to the freezing barrel, a dasher positioned in the freezing barrel for driving product through and dispensing the product from the freezing barrel, and a refrigeration system for chilling the freezing barrel. A user interface allows an operator to select from among a plurality of production rates. A system controller automatically controls the pumping rate, dasher motor speed, and chilling level to produce a product in the freezing barrel at the desired production rate and having the desired product quality and consistency. An ultrasonic sensor may be employed to monitor a level of liquid mix in a liquid mix container. A warning signal may be provided to the operator when the level of mix in the container runs low.