In a mixing bowl, whisk together heavy cream, whole milk, and granulated sugar until the sugar is dissolved.
Add the pure vanilla and peppermint extracts, mixing well.
If desired, add green food coloring until the desired color is reached.
Stir in the semi-sweet chocolate chips.
Pour the mixture into an ice cream maker.
Churn according to the manufacturer's instructions, usually about 20-25 minutes.
Transfer the ice cream to an airtight container.
Smooth the top and cover with plastic wrap before sealing the lid.
Freeze for at least 4 hours or until firm.
Scoop and serve, garnished with extra chocolate chips or mint leaves if desired.