In a medium saucepan, combine heavy cream, milk, ½ cup sugar, and salt.
Add spearmint leaves to the saucepan and heat over medium heat until mixture almost comes to a boil.
Remove from heat, cover, and let steep for about 30 minutes.
In a separate bowl, whisk egg yolks with remaining ¼ cup of sugar until pale and slightly thickened.
Slowly pour the cream mixture into the egg yolks while whisking constantly.
Return mixture to saucepan and cook over low heat, stirring constantly, until mixture thickens and coats the back of a spoon.
Strain the mixture through a fine-mesh sieve to remove the spearmint leaves.
Stir in vanilla extract.
Chill the mixture in the refrigerator for at least 4 hours or overnight.
Once chilled, churn the mixture in an ice cream maker according to the manufacturer's instructions.
Transfer the churned ice cream to a container and freeze until firm.
