In a large saucepan, combine the heavy cream, whole milk, and 1/2 cup plus 2 tablespoons of granulated sugar.
Bring the mixture to a boil, stirring until the sugar dissolves, which should take about 5 minutes.
Remove the saucepan from heat.
In a medium bowl, whisk together the egg yolks and the remaining 1/2 cup plus 2 tablespoons of granulated sugar until the mixture is smooth, thick, and pale yellow, approximately 30 seconds.
Gradually whisk about half of the hot cream mixture into the egg yolks, then whisk the egg yolk mixture back into the remaining hot cream in the saucepan.
Cook over low heat, stirring constantly until the ice cream base coats the back of a spoon and registers between 165° and 180° on an instant-read thermometer, approximately 2 minutes.
Strain the mixture into a large bowl, cover, and refrigerate for 12 to 24 hours.
Stir the finely chopped mint, dark brown sugar, and kosher salt into the ice cream base.
Process the mixture in an ice cream maker according to the manufacturer’s instructions.
Transfer the churned ice cream to a large bowl and stir in the mini semisweet chocolate chips.
Scrape the ice cream into an airtight container and freeze until firm, for about 3 to 4 hours.