Combine the first 6 ingredients in a medium saucepan over medium-high heat, stirring well with a whisk. Cook for 8 minutes or until thick and bubbly, stirring constantly.
Remove pan from heat. Add 1 teaspoon vanilla and chocolate, stirring until smooth. Transfer the mixture to a bowl; place bowl in an ice-filled bowl. Cover surface of pudding directly with plastic wrap; cool completely. Spoon chocolate mixture evenly into 6 (4-ounce) ice-pop molds. Top with lid; insert craft sticks. Freeze 4 hours or until thoroughly frozen.