Heat heavy cream and half-and-half in a heavy-bottomed saucepan over medium-low heat until barely simmering, stirring frequently. Reduce heat to low.

Whisk egg yolks, sugar, and salt together in a large bowl until thoroughly combined.

Slowly pour about 1/2 cup of hot cream mixture into egg yolk mixture, whisking constantly. Repeat three times more, whisking thoroughly before adding each additional 1/2 cup of hot cream to egg yolk mixture. Pour egg yolk mixture back into the saucepan with 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.