Place the sugar, cocoa, and salt in a large mixing bowl, and whisk to combine.
Add the cream cheese, mixing on medium-low speed until combined.
Add the eggs and yolks, one at a time, stopping to scrape the bottom and sides of the bowl with a silicone spatula after each addition.
Stir in the cream, melted chocolate, and vanilla, and transfer the cheesecake batter to the prepared pan.
Rap the unbaked cheesecake sharply on the counter a few times, to eliminate any large air bubbles.
Place it in a larger baking dish, and pour very hot water into the larger dish until it comes up about 1-inch around the cheesecake pan.
Bake for 20 minutes at 350 degrees F, then lower the oven temperature to 250 degrees F, and bake for another 65 minutes, or until set around the edges but still slightly jiggly towards the center.
Turn off the oven, and prop the door open with a wooden spoon. Allow the cheesecake to cool slowly in the oven for at least an hour.
Refrigerate for 2 hours to overnight before flipping out of the pan and onto a serving plate. (Wrap in a hot towel to help release the cheesecake from the pan.)