In a small sauce pan heat the butter over medium high heat until melted and golden brown, being careful not to burn and stirring often.
Add the cream and 1 cup of milk and heat until scalding (not quite boiling).
In a separate bowl whisk together the brown sugar and egg yolks until light and fluffy.
Slowly pour about half of the butter mixture into the egg mixture, whisking constantly. Pour back into the saucepan and add the pinch of salt. Heat to 170 degrees, or until a custard forms that coats the back of a spoon. Stir in the vanilla.
Transfer the custard to a bowl and cover with plastic wrap. Refrigerate overnight to chill completely.
Remove from the refrigerator and whisk in the remaining cup of milk.
Pour into ice cream maker and freeze according to manufacturers directions. During the last few minutes of freezing add small pieces of cookie dough.
To make the cookie dough:
Beat together the butter and sugars until light and fluffy.
Beat in the milk and vanilla.
Mix in the flour until well combined.
Stir in the chocolate chips.
Break into small pieces with your fingers to add to the ice cream.