In a medium saucepan, heat the cream, milk, 1/2 cup sugar and the mint over medium heat, stirring, until almost simmering, about 5 minutes. Remove from the heat, cover and let stand for 15 minutes.
In a bowl, whisk the egg yolks, remaining 1/2 cup sugar and the salt. Add the hot liquid to the egg mixture in a slow stream, whisking constantly; pour into the saucepan. Cook over medium-low heat, stirring, until the custard thickens and registers 175° on an instant-read thermometer, about 8 minutes.
Strain the custard into a bowl set in an ice water bath. Stir in 1 to 2 drops food coloring, if using. Let cool, then cover and refrigerate for at least 4 hours.
Using an ice cream machine, process the custard according to the manufacturer’s instructions. Fold in the chocolate chips, then transfer to an airtight container and freeze until firm, about 4 hours.