In a small bowl, whisk together chocolate milk, pudding mix, cocoa powder, vanilla extract, and sweetener until fully combined.
Pour the mixture into a Ninja Creami pint container and place it in the freezer. Let freeze for at least 24 hours.
After freezing, install the pint into the Ninja Creami machine and spin using the 'Lite Ice Cream' setting.
If the texture is crumbly, add 1 tablespoon of chocolate milk and re-spin until creamy.
Serve immediately or store in the freezer for up to 2 weeks.