In a large bowl, whisk together the heavy cream, whole milk, granulated sugar, 1 teaspoon vanilla extract, and salt until fully combined. Set aside.
In a separate bowl, mix the softened butter and brown sugar together until creamy. Add 1 teaspoon of vanilla extract and 1 tablespoon of milk, mixing well. Gradually incorporate the all-purpose flour until a dough forms. Fold in the mini chocolate chips. Set aside.
Pour the ice cream base into an airtight container and refrigerate for about 2 hours or until it is thoroughly chilled.
Once the base is chilled, pour it into an ice cream maker and churn according to the manufacturer's instructions until it reaches a soft-serve consistency.
Take the cookie dough you prepared and break it into small chunks. Gently fold these chunks into the churned ice cream.
Transfer the ice cream to an airtight container and freeze for at least 4 hours, or until firm.
Once the ice cream is firm, scoop it into bowls or cones and enjoy your homemade chocolate chip cookie dough ice cream!
Notes
For best results, ensure the ice cream base is thoroughly chilled before churning.