Combine cream, milk, sugar, and salt in a saucepan over medium-low heat. Simmer until the sugar dissolves, about 5 minutes.

In a separate bowl, whisk the egg yolks. Gradually drizzle about 1/2 cup of the warm milk mixture into the yolks, whisking constantly.

Return the tempered yolks to the saucepan and add the vanilla. Cook over medium-low heat, stirring constantly, until the mixture thickens and coats the back of a spoon. Do not let the mixture boil at any point.

Strain the mixture through a mesh sieve, then cool to room temperature. Cover and refrigerate until completely chilled, about 3-4 hours.

Churn in an ice cream maker according to the manufacturer's instructions.