01 - Combine heavy cream, whole milk, and half of the sugar in a medium saucepan. Heat over medium heat until mixture is steaming but not boiling, stirring occasionally to dissolve sugar.
02 - Whisk egg yolks with remaining sugar in a mixing bowl until mixture becomes pale yellow and slightly thickened, about 2-3 minutes.
03 - Gradually ladle approximately 1 cup of hot milk mixture into egg yolks while whisking continuously. This prevents eggs from scrambling when added to hot liquid.
04 - Return tempered egg mixture to saucepan. Cook over low heat, stirring constantly with wooden spoon, until custard thickens enough to coat back of spoon (170-175°F). Do not let mixture boil.
05 - Remove from heat immediately. Stir in peppermint extract, vanilla extract, and green food coloring until fully incorporated and color is uniform throughout.
06 - Pour custard through fine mesh sieve into clean bowl to remove any cooked egg bits. Cool to room temperature, then cover surface directly with plastic wrap. Refrigerate at least 4 hours or until completely cold, preferably overnight.
07 - Process chilled custard in ice cream maker according to manufacturer's instructions. During last 2-3 minutes of churning, add chopped chocolate chips through feed tube.
08 - Transfer churned ice cream to freezer-safe container, pressing plastic wrap directly onto surface to prevent ice crystals. Freeze at least 2 hours until firm enough to scoop.
09 - Scoop into bowls or cones. Let soften 2-3 minutes at room temperature before serving for optimal texture. Garnish with fresh mint leaves if desired.