Prepare an ice-water bath and set aside. Bring milk and cream to a boil in a heavy-bottomed saucepan over medium-high heat.
Meanwhile, in a medium bowl, whisk yolks and sugar together until well combined and slightly thickened. Slowly whisk in 1/3 of the hot milk mixture until egg mixture is slightly heated, then continue whisking remaining milk mixture into egg mixture. Return mixture to saucepan and place over medium heat; cook, stirring, until mixture is thick enough to coat the back of a spoon and reaches between 170 and 180 degrees on an instant-read thermometer.
Remove from heat and strain into a bowl; stir in vanilla. Place bowl in ice-water bath and stir to cool, about 20 minutes. Remove bowl from ice-water bath and cover; transfer to refrigerator for at least 24 hours and up to 3 days before using.