Combine the chocolate milk, sugar and cocoa powder in a stand mixer. Whisk until the sugar dissolves.
Add the heavy cream and vanilla. Whisk until the mixture thickens.
Add the food colouring and mix on slow until combined.
Cover the mixing bowl and place in the fridge for a minimum of 1 hour, or preferably overnight. The red colour will deepen overnight.
Remove the bowl from the fridge, uncover and transfer the liquid to an (frozen) ice cream maker bowl. Place on machine and begin to churn. You will want to churn this for about 10 to 15 minutes. Remove and place in freezer for 1 hour, over overnight.
If you don't have an ice cream maker pour the liquid into a metal container and place in the freezer for a minimum of 4 hours, or overnight. It will just be a tad softer than if you used the ice cream maker.
Serve with a big old red velvet smile!