Preheat the oven to 350°F. Grease the bottom and sides of a 9-inch springform pan and line the bottom with parchment paper.
In a medium bowl, whisk together the melted 1/2 cup butter and 1 cup sugar for the brownie base until glossy and well combined.
Whisk in the 2 eggs and 1 teaspoon vanilla bean paste for the brownie base until smooth.
In a separate bowl, whisk together 1/3 cup cocoa powder, 1/2 cup flour, 1/4 teaspoon salt, and 1/4 teaspoon baking powder until evenly combined.
Add the dry ingredients to the wet brownie mixture and stir just until no streaks of flour remain.
Spread the brownie batter evenly into the prepared springform pan and smooth the top with a spatula.
Bake the brownie base for 20 to 25 minutes, until the edges are set and a toothpick inserted near the center comes out with a few moist crumbs.
Remove the pan from the oven and let the brownie base cool completely in the pan on a wire rack.
Reduce the oven temperature to 325°F.
In a large mixing bowl, beat the softened cream cheese on medium speed until completely smooth and creamy, scraping down the bowl as needed.
Gradually add 1 cup sugar for the cheesecake filling while mixing on medium speed until fully incorporated and smooth.
Add the sour cream and 1 cup heavy cream for the cheesecake filling and mix until the batter looks silky and well combined.
Add the 4 eggs for the cheesecake filling one at a time on low speed, mixing just until each egg is incorporated before adding the next.
Mix in the 2 teaspoons vanilla bean paste for the cheesecake filling on low speed until evenly distributed.
Pour the cheesecake batter gently over the cooled brownie base in the springform pan and tap the pan lightly on the counter to release any large air bubbles.
Place the springform pan in a large roasting pan and set it on the middle oven rack.
Carefully pour hot tap water into the roasting pan until it reaches about halfway up the sides of the springform pan, avoiding any splashes into the batter.
Bake the cheesecake at 325°F for 60 to 70 minutes, until the edges are set and slightly puffed but the center still jiggles slightly when gently shaken.
Turn off the oven, crack the oven door slightly, and leave the cheesecake inside for 1 hour to cool gradually.
Remove the springform pan from the water bath, discard the water, and place the pan on a wire rack to cool to room temperature.
Once the cheesecake has cooled to room temperature, cover the pan and refrigerate for at least 4 hours or overnight until thoroughly chilled and firm.
When ready to top with hot fudge, make the sauce by whisking together 1/2 cup sugar, 1/2 cup cocoa powder, and a pinch of salt in a small saucepan.
Add the 1/4 cup butter for the hot fudge to the saucepan and place over medium heat, stirring until the butter is melted and the mixture forms a thick, smooth paste.
Slowly whisk in the 1/2 cup heavy cream for the hot fudge, stirring constantly until the mixture becomes smooth and glossy.
Bring the hot fudge mixture just to a gentle simmer, then reduce the heat and cook for 2 to 3 minutes, stirring frequently, until slightly thickened.
Remove the saucepan from the heat and stir in the 1/2 teaspoon vanilla bean paste for the hot fudge.
Allow the hot fudge to cool for 10 to 15 minutes, until warm but not hot and pourable.
Remove the chilled cheesecake from the refrigerator and run a thin knife around the edge of the pan to loosen, then release and remove the springform ring.
Pour the warm hot fudge over the top of the cheesecake, spreading it evenly to the edges with an offset spatula.
Refrigerate the cheesecake for 15 to 20 minutes to let the hot fudge set slightly.
Just before serving, garnish the top of the cheesecake with swirls of whipped cream, maraschino cherries, crushed nuts, and chocolate shavings or sprinkles.
Slice with a sharp knife, wiping the blade between cuts, and serve chilled.