We like bittersweet chocolate here, but if you prefer a sweeter pudding, omit the espresso powder and use a high-quality milk chocolate. Be sure to cook until bubbling; the cornstarch and the starch in the cocoa will prevent curdling. If you like, serve the pudding with whipped cream.
Stir together vanilla and espresso powder in bowl; set aside. Whisk sugar, cocoa, cornstarch, and salt together in large saucepan. Whisk in cream and yolk until fully incorporated, making sure to scrape corners of saucepan. Whisk in milk until incorporated.
Place saucepan over medium heat; cook, whisking constantly, until mixture is thickened and bubbling over entire surface, 4 to 6 minutes. Cook 30 seconds longer, remove from heat, add butter and chocolate, and whisk until melted and fully incorporated. Whisk in vanilla mixture.
Pour pudding through fine-mesh strainer into bowl. Press lightly greased parchment paper against surface of pudding and place in refrigerator to cool, at least 1½ hours or up to 2 days. Whisk pudding briefly and serve.
