In a large bowl, whisk together heavy cream, whole milk, and sugar until dissolved.
Add vanilla and peppermint extracts, and mix well.
If desired, add green food coloring for color.
Mix in chocolate chips until evenly distributed.
Cover and chill the mixture in the refrigerator for at least 2 hours.
Pour the mixture into an ice cream maker.
Churn according to manufacturer instructions until soft-serve consistency.
Transfer to an airtight container and freeze for 4-6 hours until firm.
Serve in bowls or cones, garnished with fresh peppermint leaves if desired.