In a mixing bowl, combine the heavy cream, whole milk, and granulated sugar. Whisk until the sugar is completely dissolved.
Add the vanilla extract to the mixture and stir well.
Cover the bowl with plastic wrap and refrigerate the ice cream base for at least 2 hours to chill thoroughly.
While the ice cream base is chilling, prepare your cookie dough chunks. You can use store-bought cookie dough or make your own by following your favorite cookie dough recipe. Cut the dough into small chunks and set aside.
Once the ice cream base is thoroughly chilled, pour it into your ice cream maker and churn according to the manufacturer's instructions. This usually takes around 20-25 minutes.
During the last few minutes of churning, add the cookie dough chunks to the ice cream. The machine will mix them evenly throughout the ice cream.
Once the ice cream is ready, transfer it to an airtight container and freeze it for an additional 2-4 hours to firm up.