In a mixing bowl, beat the sugar into the eggs until it is pale yellow. Beat in the flour and salt and set aside.
Bring the milk to a simmer in a heavy saucepan. Slowly beat hot milk into the eggs and sugar mixture. Pour the entire mixture back into the pan and place over low heat. Stir constantly with a wooden spoon until the custard thickens slightly. Do not let the mixture boil.
Remove from heat. Strain the custard into a clean bowl. Cool slightly then refrigerate until cold or overnight.
Stir the custard. Turn machine on and freeze according to your machine's instructions.
Add the maraschino cherries when the ice cream is semi-frozen and allow the machine to mix the fruit inches.
The ice cream will be soft and ready to eat. If you like firmer ice cream, transfer to a freezer container and freeze for at least 2 hours.