Working over a large bowl, sift 1/2 cup of the sugar with the cocoa, cornstarch and salt. Whisk in 1/2 cup of the milk to make a smooth paste; scrape the bottom of the bowl with a rubber spatula to be sure everything is well mixed.

Put the chocolate in a heatproof bowl. In a medium saucepan, combine the heavy cream with the remaining 1 1/2 cups of milk and 1/4 cup of sugar and bring just to a simmer over moderately high heat, stirring. Reduce the heat to moderately low and stir in the cocoa paste. Whisking constantly, boil the mixture for 1 minute. Strain the mixture over the chocolate in the bowl. Add the vanilla and stir until the pudding is smooth.

Pour the pudding into six glasses or 1-cup ramekins and let cool to room temperature. Cover the puddings and refrigerate until set, at least 4 hours. The puddings can be refrigerated for up to 2 days.