Warm the cream, milk, sugar, and mint in a saucepan until steaming. Remove from the heat, cover, and steep 30 minutes. Strain and return the cream to a clean pan.

Whisk the egg yolks with salt. Slowly whisk 1/2 cup of the warm cream into the yolks, then pour the yolk mixture back into the saucepan.

Cook over medium-low, stirring constantly, until the custard coats the back of a spoon and reaches 170°F (77°C), about 8 to 10 minutes.

Strain custard into a bowl, stir in vanilla and peppermint extract if using. Cool over an ice bath, then refrigerate until completely cold, at least 4 hours.

Churn the cold custard in an ice cream maker until soft-serve consistency, 20 to 25 minutes. Fold in chocolate chips now if you like.

Transfer to a container, press plastic wrap on top, and freeze until firm, at least 4 hours. Scoop and serve in bowls or cones.