Microwave the cream cheese for about 10 seconds until softened. Whisk in the sugar and vanilla until smooth.
Slowly whisk in the heavy cream and whole milk until the sugar dissolves.
Pour into an empty Ninja Creami pint without going past the max fill line. Cover and freeze on a level surface for 24 hours.
Remove the pint from the freezer and take off the lid. Create a 1½-inch-wide well down to the bottom of the pint.
Add the milk, half of the cake pieces, and 1 tablespoon of sprinkles to the well.
Place the pint in the outer bowl, lock the lid, and run the MILKSHAKE program.
For extra cake chunks, create a new well, add the remaining cake, and run the MIX-IN program.
Pour into glasses and top with whipped cream, sprinkles, and a cherry. Serve immediately.