Whisk all ice cream batter ingredients together in a bowl until mixture starts to thicken about 2 minutes, mixture will still be runny but should coat the back of a wooden spoon.
Making the ice cream: Make sure ice cream maker bowl is frozen and ready to use before you begin making the ice cream mixture. Pour ice cream mixture into ice cream maker and churn until the consistency of soft serve ice cream. Scoop half of the ice cream in to a freezer safe container, sprinkle one cup of cookie dough nuggets over the ice cream and repeat. (Any nuggets you have left over you can use as topping or for eating!) Freeze for two hours before serving.