Melt your chocolate in the microwave on 50 percent power for increments of 30 seconds, stirring after each until the chips have melted and smoothed. Combine the melted chocolate, sugar, cocoa powder, milk and cornstarch in a medium saucepan over medium heat. Stir frequently as the mixture cooks for about 10 minutes.
Remove from heat and add vanilla and butter until well combined. Let the cooked mixture cool slightly and pour into 8 popsicle molds. Freeze for 30 minutes and insert sticks. Now freeze completely before serving.