Whisk the sugar, cocoa, cornstarch, and salt together in a heavy medium-sized saucepan. Add 1/4 cup milk and whisk to form a smooth paste. Whisk in the remaining milk and the cream.

Whisk constantly over medium heat, scraping the bottom, sides, and corners of the pan, until the pudding thickens and begins to bubble at the edges, about 5 minutes.

Continue to cook and stir for 1 minute, then add the chocolate and whisk briskly until melted and smooth, about 30 seconds longer.

Remove from the heat and stir in the vanilla and rum, if using.

Divide the pudding among the cups or ramekins. Cover with plastic wrap.

Serve warm or at room temperature or chilled. The pudding can be covered and refrigerated for up to 3 days.