In a heavy saucepan, whisk together the yolks, sugars, salt, 1 cup of the cream, and the milk. Heat over medium-low heat just until the mixture barely comes to a boil, whisking constantly.

Pour the hot mixture through a metal mesh sieve to remove any lumps. Add the remaining cup of cream and the vanilla.

Chill for 4-6 hours, or overnight.

While the mixture chills, make the cookie dough.

Cook the butter in a saucepan over medium heat until it foams and turns light brown. Pour into a medium bowl. Stir in the brown sugar.

Add the dry pudding mix, vanilla, and cream. Stir until well combined. Mix in the flour and salt, then the chocolate chips.

Drop dough by small spoonfuls onto a plate or cookie sheet. (Or roll into tiny balls.) Freeze.

To make ice cream, pour the cold ice cream base into your ice cream machine and churn according to manufacturer's instructions.

Layer the ice cream and frozen cookie dough chunks in a freezer safe container. Let freeze for 2-3 hours, or until firm enough to scoop.