Preheat oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners.
In a bowl, whisk melted butter and 1 cup sugar. Whisk in 2 eggs and vanilla extract. Fold in cocoa powder, flour, and salt until just combined.
Divide brownie batter among muffin cups. Bake for 10-12 minutes. Remove from oven and lower temperature to 325°F (160°C).
Beat cream cheese until smooth. Gradually add 1/2 cup sugar. Mix in 1 egg, vanilla, and sour cream on low speed until just combined.
Spoon cheesecake batter over the warm brownie bases. Bake at 325°F for 15-18 minutes until edges are set.
Turn off oven, leave door cracked, and let sit for 10 minutes. Cool completely on a wire rack, then chill in the refrigerator for at least 4 hours before serving.