In a mixing bowl, combine sugar and egg yolks together. Beat the mixture until it is a thick yellow paste and set it aside.
Bring the half-and-half and milk to a simmer in a heavy, medium-size saucepan. Slowly beat the hot half-and-half and milk mixture into the egg and sugar mixture. This mixture should be hot, but not boiling. If it gets too hot or you add the egg and sugar too fast you will have scrambled eggs. Return the mixture to the saucepan and simmer for a few minutes as you constantly stir to make a custard-like consistency. Strain the mixture into a large bowl to chill overnight in a refrigerator.
The next day, stir in heavy cream and vanilla before adding it to your ice cream machine. Follow the ice cream machine's directions to freeze ice cream.
Ice cream is actually best right from the ice cream maker, when it is about 10 to 15 degrees F. If you can serve the ice cream right after it is made, it will have a soft and creamy texture like no other. You can adjust the above recipe by adding fruits, or even sweetened chocolate, to taste. When adding fruits to ice cream, blend them slightly with a food processor and sprinkle with sugar to enhance flavor. Let the fruit rest overnight with the original egg and cream mixture. Add the fruit in place of the vanilla.