In a saucepan, whisk together the sugar, cornstarch, cocoa, espresso powder, and salt. Combine milk and vanilla extract in a large measuring cup. Whisk the liquid mixture into the dry ingredients in the saucepan until smooth.

Place the saucepan over medium heat. Cook, whisking constantly, until the mixture comes to a boil and thickens, about 5 minutes. Add the chocolate and cook, whisking constantly, until the chocolate is melted, 1 to 2 minutes. Remove the saucepan from the heat. Divide the mixture equally among 6 serving dishes such as dessert coupes or ramekins. Place plastic wrap directly on the surface of each pudding to prevent a skin from forming.

Chill in the refrigerator until set, about 1 hour. Garnish with chopped cacao nibs. Serve chilled.