In a medium-sized, heavy-bottomed saucepan, combine the sugar, cocoa powder, cornstarch, and salt. Gradually pour in half of the milk, whisking thoroughly until the dry ingredients dissolve and the mixture is silky smooth. Slowly incorporate the remaining milk, continuing to whisk to ensure no lumps form.

Place the saucepan over medium heat and whisk continuously as the mixture heats up. In about 8 minutes, the pudding will begin to thicken and bubble. Allow the pudding to boil for an additional minute, ensuring you whisk constantly to prevent any scorching.

Remove the pan from the heat and immediately stir in the finely chopped chocolate and vanilla extract. Whisk until the chocolate has completely melted, and the pudding takes on a rich, smooth consistency.

Transfer the pudding to a medium bowl. To prevent a skin from forming on the surface, gently press a sheet of plastic wrap directly onto the pudding. Place the bowl in the refrigerator and let the pudding chill for 5 to 6 hours, or until fully set.

Once chilled, whisk the pudding briefly to restore its creamy texture. Divide it evenly into 4 dessert bowls or glasses. Add a generous dollop of whipped cream on top for an elegant finishing touch, if desired. Serve immediately and savor every spoonful of this velvety chocolate delight.