1. Preheat the oven to 325°F 165°C. Grease a 9-inch springform pan, line the bottom with parchment, and wrap the outside of the pan with a double layer of heavy-duty foil to protect it from the water bath.

2. Place a large roasting pan on the middle rack of the oven so it can preheat along with the oven. This will hold the water bath later.

3. Make the brownie crust: In a medium bowl whisk together the melted butter, granulated sugar, and brown sugar until glossy. Whisk in the eggs one at a time, then the vanilla.

4. In a separate bowl stir together the flour, cocoa powder, and salt. Fold the dry ingredients into the wet mixture just until combined and no streaks of flour remain.

5. Spread the brownie batter evenly into the prepared springform pan. Bake for 15 minutes, just until the top looks set but the center is still soft. Remove from the oven and let it cool for 5 to 10 minutes while you prepare the cheesecake filling.

6. Make the cheesecake layer: In a large mixing bowl beat the cream cheese until completely smooth and fluffy, scraping down the sides of the bowl. Add the granulated sugar and beat until well combined.

7. Mix in the sour cream and vanilla extract until smooth. Sprinkle in the flour or cornstarch and mix on low speed just until incorporated.

8. Add the eggs one at a time, mixing on low speed after each addition only until the egg disappears into the batter. Do not over-mix or the cheesecake can crack.

9. Pour the cheesecake batter over the slightly cooled brownie crust and smooth the top with a spatula.

10. Set the foil-wrapped springform pan into the hot roasting pan in the oven. Carefully pour hot water into the roasting pan until it comes about halfway up the sides of the springform pan to create a water bath.

11. Bake the cheesecake for 50 to 60 minutes, or until the edges look set and the center still jiggles slightly when you gently shake the pan.

12. Turn off the oven, crack the door open, and let the cheesecake rest in the warm oven for 45 to 60 minutes to cool slowly. This helps prevent large cracks.

13. Remove the springform pan from the water bath, discard the foil, and place the pan on a wire rack. Cool the cheesecake completely to room temperature.

14. Cover the pan and refrigerate the cheesecake for at least 4 hours or overnight, until fully chilled and firm enough to slice cleanly.

15. Make the hot fudge: Place the chocolate chips in a heat-safe bowl. In a small saucepan heat the heavy cream and corn syrup or butter over medium heat until just beginning to simmer.

16. Pour the hot cream mixture over the chocolate chips and let it stand for 2 to 3 minutes, then whisk until the chocolate is completely melted and the sauce is smooth and glossy. Whisk in the vanilla. Let cool until thickened but still pourable.

17. Make the whipped cream: In a chilled mixing bowl beat the cold heavy cream, powdered sugar, and vanilla extract until medium-stiff peaks form. Do not over-beat.

18. Release the sides of the chilled cheesecake by running a thin knife around the edge of the pan, then unclasp the springform and transfer the cheesecake to a serving platter.

19. Spoon warm hot fudge over the top of the cheesecake, letting it drip down the sides in thick ribbons.

20. Pipe or dollop whipped cream on top of the cheesecake in swirls or mounds.

21. Sprinkle chopped nuts and brownie chunks or chocolate pieces over the whipped cream and hot fudge.

22. Finish with maraschino cherries on top of each mound of whipped cream or in the center of the cheesecake. Slice and serve chilled with extra hot fudge on the side if you like.