In a mixing bowl, whisk together the heavy cream, whole milk, granulated sugar, vanilla extract, and peppermint extract until the sugar is dissolved.

If desired, add a few drops of green food coloring to achieve a minty color.

Cover the bowl and refrigerate the mixture for at least 2 hours or until thoroughly chilled.

Pour the chilled mixture into an ice cream maker and churn according to the manufacturer's instructions until it reaches a soft-serve consistency.

During the last few minutes of churning, add the chocolate chips to the mixture.

Transfer the churned ice cream to a freezer-safe container and freeze for at least 2 hours to firm up.