Whisk together whole milk, heavy cream, sweetened condensed milk, cocoa powder, sugar, and vanilla extract in a large bowl until smooth and no lumps remain.
Pour the mixture into a shallow freezer-safe container and freeze for 2 hours, stirring every 30 minutes to break up ice crystals.
Transfer the semi-frozen mixture to a blender and blend on high for 30 to 45 seconds until thick and creamy like soft-serve.
Serve immediately for the signature thick shake texture, or freeze for 15 more minutes if a firmer consistency is preferred.