Whisk the dry base: In a medium saucepan (off heat), whisk sugar, cocoa powder, cornstarch, salt, and espresso powder until no cocoa lumps remain. This prevents clumps later.

Add the milk slowly: Pour in about 1/2 cup milk and whisk to make a smooth paste. Gradually add the remaining milk, whisking until fully combined and smooth.

Cook to thicken: Set the pan over medium heat. Whisk constantly, scraping the corners of the pan to prevent scorching. After 5–8 minutes, the mixture will steam, then thicken and begin to bubble.

Simmer briefly: Once it bubbles, reduce heat to medium-low and continue whisking for 1–2 minutes. This cooks out the raw cornstarch taste and sets the texture.

Off heat, add chocolate: Remove from heat. Add the chopped chocolate and butter. Let sit for 30 seconds, then whisk until glossy and fully melted.

Finish with vanilla: Whisk in the vanilla. Taste and adjust salt if needed. The pudding should be thick but pourable.

Strain for extra silkiness (optional): For a restaurant-smooth finish, pass the hot pudding through a fine-mesh strainer into a bowl or large measuring cup.

Portion and cover: Divide into ramekins or bowls. Press plastic wrap directly onto the surface to prevent a skin, unless you like the old-school skin.

Chill or serve warm: Chill at least 2 hours for a firm, cool set, or serve warm after resting 10 minutes for peak coziness.

Garnish: Top with lightly sweetened whipped cream, shaved chocolate, or fresh berries. A sprinkle of flaky sea salt makes the chocolate pop.