Whisk the milk, heavy cream, sugar, pudding mix, vanilla, and salt until the sugar dissolves.
Pour into a Ninja Creami pint container below the max fill line, seal, and freeze level for 24 hours.
Cut the edible cookie dough into small, pea-sized pieces and keep chilled.
Set the frozen pint in the machine and run the Ice Cream function.
If crumbly, add 1 tablespoon of milk and run Re-Spin until smooth.
Make a hole in the center, add the cookie dough and chocolate chips, and run the Mix-In function.
Scoop, top with extra dough and chips, and serve right away.