In a saucepan over medium heat, combine the whole milk, heavy cream, and the seeds from the vanilla bean. Bring to a simmer.
In a separate bowl, whisk together the brown sugar and egg yolks until smooth. Slowly whisk in the hot cream mixture.
Return the mixture to the saucepan and cook over low heat until it thickens slightly, about 10 minutes. Remove from heat and let cool.
Chill the mixture in the refrigerator for at least 2 hours, then churn in an ice cream maker according to manufacturer's instructions.
For the cookie dough, mix together the flour, salt, baking soda, butter, granulated sugar, brown sugar, vanilla, and milk until combined. Fold in the chocolate chips.
Once the ice cream is churned, fold in chunks of cookie dough and place in a container to freeze until firm.
