In a bowl, whisk together half of the sugar, egg yolks and corn syrup.
In a large saucepan, heat the remaining sugar, milk and cream until very hot.
Gradually whisk the milk mixture into the egg yolks, then pour everything back into the saucepan and whisk over low heat until mixture thickens slightly and coats the back of a spoon. I like to cook it to 170 degrees F.
Pour mixture into a bowl. Add a pinch of salt and the Mexican vanilla. Let cool at room temperature for about an hour, then cover and chill overnight or until very cold.
Freeze in the ice cream maker following manufacturer's directions.
Notes
You can leave out the corn syrup and use an equal amount of sugar instead. I think the corn syrup helps curb the chalkiness of homemade ice cream and keeps it a little softer (though it will still need to sit a bit before you serve it).