In a small saucepan, combine sugar, cocoa, and cornstarch thoroughly.

Add cold milk and stir until the mixture is completely smooth.

Cook over medium heat, stirring constantly, until the mixture comes to a boil.

Once boiling, continue to cook for 1 minute, stirring, until it thickens.

Remove from heat and stir in the chocolate chips until fully melted and smooth.

Whisk in the vanilla extract until fully incorporated.

Spoon pudding into dessert dishes and refrigerate for at least 2 hours until chilled.