Combine milk, cream, sugar, cornstarch, and cocoa powder in a medium to large saucepan. Whisk until thoroughly combined.
Place on medium-low to medium heat and bring to a boil, stirring continuously.
Add chocolate and reduce heat, bringing the mixture down to a simmer, stirring frequently until mixture thickens (5-8 minutes). It should thicken to the point of sticking to the back of a spoon.
Chill for 2-4 hours
Follow your ice cream maker's directions for gelato to freeze or place in a freezer-safe container and into a freezer for 4-8 hours, hand-churning every 30 minutes