For the cookie dough using a hand mixer beat together the butter and the brown sugar until fluffy and grain-free, mix in the flour, 1/2tsp vanilla bean extract, all of the chocolate chips, form the dough into a log, wrap it in plastic and refrigerate until firm. Once chilled, unwrap the log and chop it into bite-sized pieces. Place the dough pieces into a freezer-safe container and into the freezer until ready to fold into the ice cream.
Dissolve the cornstarch in 50ml whole milk, leave to rest.
In a small saucepan over medium heat combine the heavy cream, the leftover milk, sugar and a pinch of salt, bring to an almost boil, add the cornstarch milk and cook constantly stirring until thickened. Take off heat, whisk in the cream cheese, cool to room temp and transfer into the fridge overnight.
Freeze in your ice cream maker according to the manufacturer's instructions adding 1/2tsp vanilla extract at the first and as many dough pieces as your common sense will allow at the last couple of minutes of churning. Store in an airtight container or spoon right away.