Put the sugar, eggs, and egg yolks in a medium-sized bowl, or in a stand mixer. Beat on medium speed for about two minutes, until the mixture is pale yellow, smooth and thick.

Put the milk and cream in a medium pan on the stove. Barely bring the mixture to a boil, then remove from heat.

Pour one cup of the hot milk and cream into a liquid measuring cup. Turn the mixer back on to medium-low speed for the eggs and sugar, and slowly pour the hot milk/cream mixture into the eggs. When thoroughly mixed, pour that entire mixture into the rest of the milk/cream mixture on the stove. Turn the heat on to medium-low, and stir constantly until mixture thickens and can coat the back of a spoon.

Transfer to a bowl, cover with plastic wrap placed directly on the custard, and chill completely for several hours.

When completely chilled, remove from refrigerator and add to your ice cream maker and follow the manufacturer's directions. Transfer to an airtight container and freeze for several hours.