Cream together the butter and sugars in a large bowl with an electric mixer on medium speed until light and fluffy (about 2-3 minutes). Gradually add in milk and vanilla. Add the flour and salt and mix on low speed until fully incorporated. Fold in chocolate chips. Set aside.
Put all of the ingredients together into a large mixing bowl and stir until well blended. Once all the ingredients have been mixed thoroughly, pour it into the assembled ice cream maker. Churn for about 20 minutes then fold in cookie dough.
If you like, you can serve the ice cream with the soft serve consistency straight out of the ice.