In a saucepan set over medium-low heat, add half-and-half, 1 ½ cups heavy cream, and sugar. Stir to dissolve the sugar.
Add the fresh mint to steep in the cream mixture while it heats.
Meanwhile, whisk the egg yolks into the remaining ½ cup heavy cream.
When the cream mixture is hot, ladle some of the hot cream into the egg yolk mixture, whisking constantly.
Slowly add the egg yolk mixture to the hot cream mixture stirring constantly. Heat over medium heat until slightly thickened. Be careful not to boil the cream.
Transfer the mixture to a heatproof bowl. Cover with plastic wrap, pressing the wrap down directly on top of the cream. Refrigerate until completely cool.
Using a mesh strainer, strain the chilled mixture into the bowl of the ice cream maker. Churn until the mixture resembles the consistency of soft serve.
Transfer to a freezer-safe container and stir in the chopped chocolate. Freeze until firm, at least 4 hours.
Notes
Yields 1 ½ quarts.
Semi-sweet chocolate can be used. Chocolate chips can also be used.
Temper the egg yolk mixture to prevent the eggs from scrambling. To do this, slowly add a ladle full of the hot cream mixture to the egg yolk mixture, whisking constantly. This brings the egg yolk mixture up to temperature. Then, add the egg yolk mixture back to the hot mixture, whisking constantly.
Strain the mixture to catch any bits of egg yolk that did not fully incorporate. This ensures a smooth ice cream.
For stronger mint flavor, strain the ice cream base after chilling, right before churning. Alternatively, strain the warm cream mixture before chilling.
If using a glass or metal container for storing the ice cream, place the container in the freezer while the ice cream churns. The cold dish will keep the ice cream cold when transferring it from the machine to the freezer.