Heat the oven to 350°F (175°C). Grease a 9-inch springform pan and line the bottom with parchment. If using a water bath, wrap the outside of the pan with two layers of heavy-duty foil.

Toast the pecans at 350°F for 6–8 minutes, watching closely so they do not burn. Cool them before chopping the amounts needed for the brownie base and topping.

Whisk the melted butter and sugar together, then beat in the eggs and vanilla. Stir in the flour, cocoa powder, and salt just until combined, and fold in 1/2 cup of chopped toasted pecans.

Spread the brownie batter evenly in the prepared pan. Bake for 15–18 minutes, until the surface is set but the center remains slightly soft, then cool for about 10 minutes.

Reduce the oven temperature to 325°F (165°C). Beat the softened cream cheese and sugar on low to medium speed until smooth, then add the eggs one at a time, mixing only until incorporated.

Blend in the sour cream, vanilla, flour, and salt. Avoid overbeating because excess air can cause cracks in the cheesecake.

Pour the cheesecake mixture over the partially baked brownie layer. Place the springform pan in a larger roasting pan and add enough hot water to reach about 1 inch up the sides, or place a pan of hot water on the lower oven rack if you are not using a water bath.

Bake at 325°F (165°C) for 50–65 minutes. The edges should look set while the center still jiggles slightly when the pan is gently shaken.

Turn off the oven, crack the door, and leave the cheesecake inside for about 30 minutes. Remove it from the water bath, cool completely, and refrigerate for at least 6 hours, preferably overnight.

Before serving, spread or drizzle the caramel over the chilled cheesecake. Scatter the remaining toasted pecans over the top, drizzle with melted chocolate, and add the optional oil if needed to make the chocolate thin enough to drizzle.