Reduce the oven temperature to 325°F.
Combine the semisweet chocolate and milk in a small saucepan or microwave-safe bowl or cup. Heat, stirring frequently until the chocolate is melted and the mixture is smooth. Stir in the cocoa powder and espresso powder, if using; set aside.
In the bowl of a stand mixer fitted with the paddle attachment beat the cream cheese and sugar on medium-low speed until smooth and creamy. Scape down the sides and bottom of the bowl and blend again on low for about 30-seconds.
With the mixer set on medium speed add the eggs, one at a time, beating just until the yolk disappears before adding the next. Scrape down the bowl and blend again. Be careful not to over mix.
Stir in the salt, vanilla, sour cream and the chocolate mixture. Blend on low until thoroughly combined. Scrape down the bowl again, and fold together using a rubber spatula.
Pour the filling over the cooled crust in the foil-wrapped springform pan. Place the roasting pan and cheesecake in the oven. Fill the outer roasting pan with enough hot tap water to come halfway up the sides of the springform pan.
Carefully slide the roasting pan into the oven. Bake at 325°F until the center jiggles slightly, the sides start to puff and the surface appears dry, about 90 to 100 minutes.
Turn off the oven and prop the oven door open slightly using a pot holder or wooden spoon. Allow the cheesecake to cool in the hot water bath for 1 hour. Transfer the cheesecake to a wire rack and remove the foil. Slide a small thin knife around the top inside edge of the pan to loosen the sides of the cheesecake. Leave the cheesecake in the pan and cool to room temperature, about 2 hours.
Once cool cover the pan tightly with plastic wrap and refrigerate overnight or up to 24 hours.