In a medium saucepan, whisk together sugar, cocoa powder, and cornstarch. Whisk in egg (mixture will be thick). Add milk and coffee, and whisk over medium heat until blended and smooth. Cook, whisking often, until mixture bubbles and thickens, about 10 minutes. Cook 1 minute longer. Remove from heat and stir in the chocolate and vanilla until the chocolate melts and incorporates.
Cool mixture slightly, and then pour into nine 2-ounce plastic ice pop molds or paper drinking cups. Insert ice pop handles, or let cool enough for wooden craft sticks or small metal spoons to stand upright. If using drinking cups, cover with plastic wrap, allowing sticks or handles to poke through the plastic. Freeze until firm, at least 2 hours or up to 2 weeks.
To unmold, run warm water around the outside of the mold until pops can be loosened free.
Tip: If you don’t like coffee, replace it with an additional cup of 2 percent milk.