01 - Combine heavy cream, milk, and half of the sugar in a medium saucepan. Heat over medium heat until just steaming, taking care not to let the mixture reach a boil.
02 - In a separate mixing bowl, whisk together egg yolks, remaining sugar, and salt until the mixture becomes pale in color and thickens in consistency.
03 - Slowly pour approximately 1/2 cup of the hot cream mixture into the egg yolks while whisking continuously. This gradual process prevents the eggs from scrambling and creates a smooth custard base.
04 - Gradually whisk the tempered egg mixture back into the saucepan with the remaining hot cream, ensuring thorough incorporation.
05 - Cook the mixture over medium-low heat, stirring constantly with a wooden spoon. Continue until the custard thickens enough to coat the back of the spoon, reaching an internal temperature of 170–175°F.
06 - Remove the saucepan from heat immediately. Stir in the peppermint extract, vanilla extract, and green food coloring if using, until fully incorporated.
07 - Pour the custard through a fine mesh sieve into a clean bowl to remove any cooked egg bits. Allow to cool to room temperature, then cover and refrigerate for a minimum of 4 hours or until completely chilled throughout.
08 - Process the chilled custard in an ice cream maker according to the manufacturer's instructions until it reaches a soft-serve consistency.
09 - During the final 2-3 minutes of churning, add the chopped chocolate chips to the machine, allowing them to distribute evenly throughout the ice cream.
10 - Transfer the churned ice cream to a freezer-safe container with a tight-fitting lid. Freeze for at least 2 hours or until the ice cream reaches a firm, scoopable texture.