Warm heavy cream, whole milk, sugar, and salt in a medium saucepan over medium heat, whisking to dissolve sugar.

Beat egg yolks in a small mixing bowl. Gradually add 1/2 cup of the warm milk mixture to the egg yolks, whisking constantly.

Return the egg yolk mixture to the saucepan. Stir in instant coffee until dissolved. Cook over medium-low heat, stirring constantly, until the mixture thickens slightly and coats the back of a spoon.

Strain the custard through a fine mesh strainer into a bowl. Stir in vanilla extract. Chill the mixture thoroughly, preferably overnight.

Churn in an ice cream maker according to the manufacturer's instructions until it reaches the consistency of soft serve.

Transfer the churned ice cream to an airtight container and freeze until firm, about 4 hours.