In a mixing bowl, combine the heavy cream, whole milk, and granulated sugar.
Whisk until the sugar is fully dissolved.
Add the vanilla extract and mix well.
Chill the mixture in the refrigerator for about 2 hours.
Pour the mixture into an ice cream maker.
Churn according to the manufacturer’s instructions until it thickens.
Add the crushed chocolate cookies during the last few minutes of churning.
Transfer the ice cream to an airtight container.
Cover and freeze for at least 4 hours or until firm.
Serve with additional cookie pieces on top if desired.