Set up the Ninja Slushi on a level counter, making sure it has sat upright at least 2 hours. Slide the condensation catch under the evaporator, click the auger into place, drop the vessel on with the bail handle up and push the handle down to lock, then snap on the drip tray.
In a 4-cup measuring cup, whisk together the vanilla ice cream, whole milk, and granulated sugar until the sugar fully dissolves and no ice cream lumps remain.
Break the Oreo cookies into pencil-eraser-sized chunks by hand, or crush them in a zip-top bag with a rolling pin. Avoid crushing to powder. Reserve a spoonful for garnish.
Pour the base through the fill port, add the cookie pieces on top, and close the cover.
Power on and select the MILKSHAKE setting. Let the machine churn 15-30 minutes, until it beeps three times and the lights go solid.
Dispense a small amount to check the texture. If it is thinner than you want, press the up arrow to increase the freeze level and wait 5 more minutes.
Pour into chilled glasses, top with whipped cream and crushed Oreos, and serve immediately with a wide straw or spoon.