Combine milk, cream, and sugar in a saucepan and heat on medium-high until simmering.
Remove from heat and whisk the yolks in a large bowl until pale.
Slowly add 1 cup of the hot milk to the yolks, all the while whisking. Once combined, whisk back into the hot milk and continue heating until the custard base thickens.
Remove the custard base from the heat and allow it to cool slightly before pulsing in a food processor – roughly six pulses are sufficient.
Add the custard base to an airtight container and refrigerate overnight, allowing the mint flavour to infuse.
Once chilled, strain and add to an ice cream machine; churn following the manufacturer's instructions.
When the ice cream is almost ready to be removed from the machine, toss in the chocolate pieces. Allow a minute for the add-ins to distribute.
Add the ice cream to an airtight container and freeze for at least 2 hours or until you get the desired hardness.