1. For the dark chocolate cream: Combine the heavy cream, salt and corn syrup in a small saucepan over medium heat; let the mixture come to a low boil (prominent bubbles will appear at the edges and center of the pan), stirring once or twice to mix well.

2. Meanwhile, place the chopped chocolate in a food processor; pulse until very finely chopped, so the chocolate will melt properly. Transfer to a medium stainless-steel mixing bowl and add the vanilla extract. Pour the hot cream mixture though a fine-mesh strainer evenly over the chopped chocolate. Let the mixture stand for 2 minutes. Use a silicone spatula or wooden spoon to stir the chocolate, starting at the center and moving slowly outward. (Do not use a whisk, which would introduce unwanted aeration.) Clean the strainer for use in the next step.

3. Pour the chocolate mixture through the fine-mesh strainer into a small bowl; the mixture should be smooth and lightly glossy. Cool, undisturbed, at room temperature for 30 minutes. Use the mixture immediately, or cool at room temperature for about 3 hours until set, then cover tightly and refrigerate.

4. For the cream topping: Chill the beater(s) of a hand mixer and a small mixing bowl.
Place the cold heavy cream in the chilled bowl and use the hand mixer with chilled beaters to beat the cream on medium speed for about 30 seconds, until it just begins to thicken. Sprinkle the sugar over it and beat for about 1 minute, until the cream has thickened but is still soft. Add the vanilla extract and beat on low speed for about 1 minute, or until the cream just holds its shape on the beater, with a moderately firm consistency. Use as much of the whipped cream as desired, reserving any extra for another use.

5. To assemble: Bring the dark chocolate cream to room temperature. Combine the milk, sugar and salt in a large saucepan on medium-low heat; warm the mixture for about 10 minutes or until the sugar dissolves, stirring often. Increase the heat to medium-high and let the mixture heat, undisturbed, for 7 to 8 minutes, until small bubbles appear around the edges of the pan.

6. Remove from the heat and add the dark chocolate cream in dollops, whisking until thoroughly incorporated. Return the saucepan to the stove, over medium heat, and whisk rapidly for 3 minutes, or until the mixture is heated through. Remove from the heat and whisk in the vanilla extract. Divide the hot chocolate among 5 cups and top with dollops of the cream topping.