To Make the Brownie Base:

1. Position a rack in the center of the oven and preheat the oven to 325°F. Lightly grease the bottom and sides of a 9 × 3-inch spring form pan. Cut an 18-inch square of heavy-duty aluminum foil and wrap the foil around the outside of the pan.

2. In the top of a double boiler, melt the chocolate with the butter over barely simmering water, stirring occasionally. Transfer the mixture to a medium bowl and stir in the espresso powder, vanilla extract, and salt. Whisk in the sugar until combined. Whisk in the eggs one at a time, until blended. Stir in the flour until no traces remain.

3. Scrape the batter into the prepared pan and smooth it into an even layer. Bake the brownie for 25 to 30 minutes, until a tooth pick inserted into the center comes out with a few moist crumbs clinging to it. Place the pan on a wire rack and let cool while you make the filling. Leave the oven on.

To Make the Filling:

4. In the bowl of an electric mixer, using the paddle attachment, beat the cream cheese at medium-low speed until creamy and smooth, about 2 minutes. Gradually add the sugar and beat until blended. Add the vanilla extract, espresso mixture, Kahlúa, salt, sour cream, and cornstarch and mix until well blended. At low speed, add the eggs one at a time, mixing well after each addition and scraping down the sides of the bowl with a rubber spatula as needed.

5. Scrape the batter onto the brownie base. Place the pan in a roasting pan or large baking pan. Pour enough hot water into the roasting pan to come about 1 inch up the sides of the springform pan. Bake the cake in the water bath for 70 to 80 minutes, until the center is set but slightly wobbly (the cake will continue to set up as it cools). Remove the pan from the water bath and cool the cake completely in the pan on a wire rack.

6. Refrigerate the cheesecake for at least 4 hours before serving.

7. To serve, slice the cake with a thin-bladed sharp knife, wiping the knife clean between each cut. Garnish each slice with a dollop of whipped cream and a few chocolate-covered espresso beans.