Place 6 cookies in the freezer for 1 hour. Transfer the cookies to a small food processor and process them into crumbs. Or, for slightly more fun, place the cookies in a zip-top bag and pound them with your fist! Set this cookie “powder” aside.
Make the milk chocolate paste: In a small saucepan, bring ⅓ cup (80 ml) water to a boil over high heat. Remove the pan from the heat and add the sugar and cocoa powder, whisking vigorously to combine. Add the chocolate and whisk until melted. Set aside to cool.
Make the chocolate milk ice cream: Prepare Walt’s Dream according to the recipe directions. Once the base reaches 165°F (75°C), remove it from the heat and mix in the cooled milk chocolate paste. Transfer the pan to the ice bath and let cool for 15 to 20 minutes. Pour the ice cream base through a wire-mesh strainer into a storage container and move to fridge for 1 to 2 hours, or until completely cool.
Transfer the cooled base to an ice cream maker and add the cookie powder. Churn the ice cream according to the manufacturer’s instructions.
Break the remaining cookies into quarters. Transfer the ice cream to a storage container, folding in the cookie pieces as you do. Serve immediately or harden in your freezer for 8 to 12 hours for a more scoopable ice cream.