1. Prepare the pan and oven by lining the bottom of a 9-inch springform pan with parchment, lightly greasing the sides, wrapping the outside in foil if using a water bath, and preheating the oven to 350°F (175°C).

2. Make the brownie batter by whisking together melted butter and granulated sugar until glossy, then adding eggs and vanilla and whisking until slightly thickened.

3. Sift in the cocoa powder, all-purpose flour, salt, and baking powder, stirring just until the batter is smooth and no dry streaks remain.

4. Bake the brownie base by spreading the batter evenly in the pan and baking for 18 to 22 minutes, or until the top looks set and a toothpick inserted near the center comes out with a few moist crumbs; let cool for 10 to 15 minutes and reduce the oven to 325°F (165°C).

5. Beat the cream cheese in a large bowl until completely smooth, scraping down the sides of the bowl to remove any lumps.

6. Add the granulated sugar and beat until the mixture is creamy and slightly fluffy, then mix in the sour cream, vanilla extract, and salt on low speed until combined.

7. Add the eggs one at a time, mixing on low after each addition just until incorporated to avoid adding too much air to the batter.

8. Assemble the cheesecake by pouring the cheesecake batter over the slightly cooled brownie base, tapping the pan gently to release air bubbles.

9. Bake the cheesecake layer at 325°F (165°C) for 55 to 65 minutes, using a water bath if desired, until the edges are set and the center still has a gentle wobble when the pan is jiggled.

10. Cool the cheesecake gradually by turning off the oven, cracking the door, and letting it sit inside for 45 to 60 minutes before transferring it to a rack to cool completely; run a knife around the edge to loosen it from the pan.

11. Chill the cheesecake covered in the refrigerator for at least 6 hours or overnight until fully set and firm enough to slice cleanly.

12. Make the hot fudge topping by heating the heavy cream until steaming, then pouring it over the semi-sweet chocolate chips and letting it sit briefly before stirring smooth.

13. Stir in the light corn syrup or unsalted butter, vanilla extract, and a pinch of salt until the mixture is glossy and slightly thickened, then let it cool to a pourable but not hot consistency.

14. Add the fudge layer by pouring the cooled chocolate mixture over the chilled cheesecake and smoothing it to the edges with an offset spatula; chill again for 30 to 45 minutes until softly set.

15. Whip the cold heavy cream with powdered sugar and vanilla extract until soft peaks form, making sure it stays smooth and not grainy.

16. Decorate the cheesecake like a sundae by piping or spooning whipped cream over the top, then adding chopped peanuts or mixed nuts, sprinkles, and maraschino cherries.

17. Slice the cheesecake with a sharp knife warmed in hot water and wiped dry between cuts, and serve each slice chilled, optionally with extra chocolate sauce or a scoop of vanilla ice cream.