In a heavy, nonreactive saucepan, stir together the sugar and cornstarch. Whisk in the milk and cream over low heat and whisk constantly until the mixture just reaches a boil -- 5 to 8 minutes or so. Set the saucepan into a large baking dish, pack ice cubes around it and add some water to the ice. Stir frequently until the mixture is as cold as you think it's likely to get.

In a food processor, puree the strawberries. Stirring hard, pass the puree through a fine sieve into the chilled custard. Stir in the salt and the red juice of your choice. If you want, taste the mixture to see if it would benefit from a little citric acid.

Refrigerate the mixture for at least 4 hours or overnight. I do this in the fridge, but of course you can keep using the baking-dish-full-of-ice method if you have unlimited ice.

Churn the batter in an ice cream maker "according to the manufacturer's instructions." And then, unfortunately you have to pack it into an airtight container and freeze it for at least 3 more hours before it's at its best.