Prepare an ice bath by putting ice and cold water in a bowl large enough to hold another bowl inside.
In a small bowl, whisk the egg yolks.
Combine the milk, cream, sugar, and pinch of salt in a saucepan. Stir to dissolve the sugar and heat over medium heat. Do not boil.
Pour a little of the warmed milk mixture into the bowl with the egg yolks, whisking constantly. Return the egg yolks to the saucepan.
Cook the custard, stirring constantly with a spatula, until the mixture thickens and coats the spatula. If you're unsure about when it is ready, you can check the temperature with an instant-read thermometer. It should read about 170°F.
Stir in the vanilla extract.
Pour the custard into a bowl and put the bowl immediately into the ice bath. Stir the custard until it cools.
Refrigerate thoroughly, preferably overnight, then freeze it in your ice cream maker following the manufacturer's instructions.
When finished, cover and freeze until firm.