F For the filling:
Dump the mixture into a 9-inch springform pan and press evenly onto the bottom and about 1 inch up the sides of the pan (to press, use plastic wrap, a straight-sided, flat-based coffee mug, or a tart tamper). Bake for 10 minutes and set on a wire rack to cool. Reduce the oven temperature to 300°F.
Make the filling: Mix the sour cream, vanilla, and coffee granules in a small bowl. Set aside and stir occasionally until the coffee dissolves.
Melt the chocolate in a double boiler over medium heat. Stir until smooth. Set aside to cool slightly.
In a stand mixer fitted with the paddle attachment, beat the cream cheese, cocoa powder, and salt until very smooth and fluffy, scraping down the sides of the bowl and paddle frequently (and with each subsequent addition). Add the sugar and continue beating until well blended and smooth. Scrape the cooled chocolate into the bowl; beat until blended. Beat in the sour cream mixture until well blended.
Add the eggs, one at a time, and beat until just blended. (Don’t overbeat the filling once the eggs have been added or the cheesecake will puff too much.)
Pour the filling over the cooled crust, spread evenly, and smooth the top.
Bake at 300°F until the center barely jiggles when nudged, 50 to 60 minutes. The cake will be slightly puffed, with a few little cracks around the edge. Let cool to room temperature on a rack and then refrigerate until well chilled, at least a few hours, or overnight for the best texture and flavor. (This cake freezes well, too: Put the unmolded cake in the freezer, uncovered, until the top is cold and firm, and then wrap it in two layers of plastic and one layer of foil.)
To serve: Unclasp the pan’s ring, remove it, and run a long, thin metal spatula under the bottom crust. Carefully slide the cake onto a flat serving plate.
Top the cake with fresh whipped cream and chocolate shavings. Run a thin knife under hot water, wipe it dry, and cut the cake into slices, heating and wiping the knife as needed.