In a large mixing bowl, combine the heavy cream, whole milk, and granulated sugar.
Whisk the mixture until the sugar is fully dissolved.
Add the vanilla extract and stir well to combine.
Gently fold in the crushed Oreo cookies.
Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions.
Transfer the ice cream to an airtight container.
Drizzle chocolate syrup on top if desired, and swirl it through the mixture.
Cover the container and freeze for at least 4 hours.
Let the ice cream sit at room temperature for a few minutes before serving.
Scoop into bowls and enjoy your homemade cookies and cream ice cream!