01 - Combine heavy cream, milk, and half of the sugar in a medium saucepan. Heat over medium heat until just steaming, not boiling.
02 - Whisk together egg yolks, remaining sugar, and salt in a separate bowl until pale and thick.
03 - Slowly pour about 1/2 cup of the hot cream mixture into the egg yolks, whisking constantly to temper the eggs.
04 - Gradually whisk the tempered egg mixture back into the saucepan.
05 - Cook over medium-low heat, stirring constantly with a wooden spoon, until the custard thickens enough to coat the back of the spoon (170-175°F).
06 - Remove from heat. Stir in peppermint extract, vanilla extract, and green food coloring if using.
07 - Pour the custard through a fine mesh sieve into a clean bowl. Let cool to room temperature, then cover and refrigerate for at least 4 hours or until thoroughly chilled.
08 - Churn the chilled custard in an ice cream maker according to the manufacturer's instructions.
09 - In the last few minutes of churning, add chopped chocolate chips.
10 - Transfer the ice cream to a lidded container and freeze for at least 2 hours, or until firm.
11 - Serve scoops in bowls or cones and enjoy immediately.