Preheat oven to 350°F (175°C). Line an 8-inch springform pan with parchment paper. Melt butter in a bowl, then stir in sugar. Add eggs and vanilla; whisk until smooth.
Mix in cocoa powder, flour, and salt until just combined. Spread batter in pan and bake for 20 minutes. Let cool slightly.
Beat softened cream cheese with sugar until smooth and fluffy. Add eggs one at a time, mixing well after each. Stir in vanilla and sour cream until fully blended. Pour cheesecake mixture over brownie base and smooth the top.
Bake at 350°F (175°C) for 45 minutes. Turn off the oven, crack the door open, and let cheesecake sit inside for 1 hour. Transfer to the fridge and chill for at least 4 hours or overnight.
In a saucepan over medium heat, melt sugar while stirring until it turns deep amber. Carefully stir in butter (it will bubble), then slowly add heavy cream and a pinch of salt.
Let it bubble for 1–2 minutes. Remove from heat and cool to room temperature.
Once chilled, remove cheesecake from pan. Pour cooled caramel over the top, letting it drip slightly over the edges. Slice with a hot knife (wipe between cuts) and serve chilled or lightly warmed.