In a mixing bowl, combine sugar, vanilla extract, and cream cheese using a wooden spoon. Mix into a thick paste.
Combine milk and heavy cream in another bowl.
Slowly add the liquid mixture to the sugar mixture, mixing to combine thoroughly. Continue until the liquid is completely mixed in and the sugar is dissolved.
Transfer everything to a Ninja Creami pint. Close and place in the freezer for 24 hours.
Remove from the freezer the next day, remove the lid, and add a pint to the bowl of Ninja Creami. Secure the lid and lock it into the machine.
Press the Ice Cream function and allow the machine to run for 2 whole minutes.
When the machine is done, unlock the bowl, take the lid off, and serve your delicious ice cream.