Preheat your oven to 350°F (175°C). Prepare a muffin tin with cupcake liners.
In a large bowl, mix melted butter and granulated sugar until well combined.
Add eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Sift in the flour and cocoa powder, folding gently until just combined.
Divide the brownie batter evenly among the lined muffin cups, filling each about halfway.
In a separate bowl, beat the softened cream cheese until smooth, then add sour cream and powdered sugar.
Spoon the cheesecake mixture over the brownie batter, filling each cup to the top.
If desired, sprinkle with chocolate chips and chopped nuts before baking.
Bake for 20-25 minutes, or until the edges are set but the centers are slightly soft.
Let cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
Chill in the refrigerator for at least an hour before serving for the best texture.