In a liquid measuring cup, combine milk, vanilla pudding mix, and sugar. Whisk well to dissolve.
Add heavy cream and vanilla extract, stirring until combined.
Pour mixture into a Ninja Creami Swirl pint container. Close the lid on the container and transfer to a level surface in the freezer. Let freeze for at least 24 hours.
Remove the container from the freezer and take off the lid. Place the pint into the outer bowl of the machine, securing the outer bowl lid.
Lock the outer bowl into place in the machine, then press "Soft Serve" followed by "Ice Cream." Allow the machine to process the ice cream.
When the machine beeps to signal its completion, remove the pint from the machine. If it's not uniformly creamy, you can insert it back into the machine and use the Re-spin button.
Remove the pint from the outer bowl, then attach the soft serve dispensing lid to the pint.
Matching the blue line on the dispensing lid with the blue line on the dispensing side of the machine, insert the pint into the machine and twist to lock it into place.
Twist the white base of the pint until it is in the "Open" position. Pull the lever of the machine to dispense the ice cream into a cone or bowl.
When you are finished dispensing, press the "Retract" button, then remove the pint from the machine. Remove the dispensing lid and attach the regular lid to store leftovers. Be sure to wash out the dispensing tube on the pint container, too.
Serve and enjoy!