Add the whole milk, heavy cream, cream cheese, maple syrup, vanilla extract, cinnamon, and salt to a blender. Blend until smooth and fully combined.
Pour the mixture into a Ninja Creami pint container, making sure not to fill past the MAX FILL line. Secure the storage lid and freeze on a level surface for at least 24 hours.
To make the cinnamon swirl, add the brown sugar, maple syrup, heavy cream, and cinnamon to a small saucepan.
Cook over low heat for 1 to 2 minutes, stirring constantly, until the brown sugar has dissolved and the mixture is smooth. Remove from the heat and transfer to a small bowl.
Let the cinnamon swirl cool completely. Refrigerate it while the ice cream base freezes if preparing it ahead of time.
Remove the frozen pint from the freezer and take off the storage lid. Place the pint in the Ninja Creami outer bowl and process using the Ice Cream setting.
If the ice cream looks powdery or crumbly after processing, add 1 tablespoon of milk and use the Re-Spin setting.
Remove the pint from the machine. Drizzle the cooled cinnamon sauce over the ice cream.
Use the Mix In setting to incorporate the sauce into the ice cream. Scoop and serve immediately.
Notes
Serving size: About 1 cup
For a dairy-free version, use oat milk, coconut cream, and dairy-free cream cheese in place of the dairy ingredients.
Make sure the cinnamon roll mix-in is completely cool before adding it to the ice cream.
If the ice cream is powdery after processing, add 1 tablespoon of milk and use the Re-Spin setting.
Store leftovers in the covered Ninja CREAMi pint container for up to 2 weeks. Smooth the top before refreezing.