Combine sugar, cornstarch, cocoa powder, and milk in a small saucepan over medium heat. Bring to a simmer and stir until thick, about two minutes. Remove from heat; stir in vanilla and butter. Transfer to a heatproof bowl and refrigerate until cool, approximately 20 minutes.
Stir chocolate chips into the cooled chocolate mixture. Pour into moulds and freeze until firm, about four hours. Yields eight servings.