Preheat oven to 350°F (175°C) and line a 12-cup muffin tin with paper liners.
Whisk melted butter and 1 cup sugar. Add 2 eggs and vanilla, mixing until thick. Fold in flour, cocoa powder, and salt.
Divide brownie batter into the muffin cups (about 1/3 full). Bake for 10 minutes. Let cool slightly.
Beat cream cheese until smooth. Gradually add 1/2 cup sugar. Add the remaining egg, vanilla, and sour cream on low speed until just combined.
Spoon the cheesecake batter over the warm brownie bases. Bake for 15-18 minutes until edges are set but centers slightly jiggle.
Cool completely in the pan for 1 hour, then refrigerate for at least 4 hours before serving.