Pour the heavy cream and half-and-half into a heavy saucepan, place over medium-low heat, and heat until barely simmering, stirring frequently. Turn the heat down to low.
Whisk together the egg yolks, sugar, and salt in a large bowl until thoroughly combined. Temper the egg yolk mixture by slowly pouring about 1/2 cup of hot cream mixture into the egg yolk mixture, whisking constantly. Repeat three times more, whisking thoroughly before adding each additional 1/2 cup of hot cream to the egg yolk mixture. Pour the egg yolk mixture back into the saucepan with the remaining hot cream, and whisk constantly over medium-low heat until the mixture thickens and will coat the back of a spoon, 5 to 8 minutes. Do not let mixture boil.
Pour the ice cream base into a bowl and allow to cool for about 20 minutes; place in refrigerator and chill overnight. The next day, pour into an ice cream maker, and freeze according to the manufacturer's directions. Remove the ice cream, pack into a covered container, and freeze for 2 hours or overnight before serving.