Preheat your oven to 350°F (175°C). Line a 24-cup standard muffin tin with paper liners.

In a large bowl, whisk together the melted butter, 1 cup of granulated sugar, and 1 teaspoon of vanilla extract. Beat in the eggs one at a time. In a separate bowl, sift together the flour, cocoa powder, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Distribute the brownie batter evenly among the 24 muffin liners, filling each about 1/4 full. Bake for 10-12 minutes. Let it cool slightly.

In a large mixing bowl, beat the softened cream cheese until smooth. Gradually add the 3/4 cup of granulated sugar. Add the eggs one at a time, mixing on low after each. Stir in the sour cream and 1 teaspoon of vanilla extract.

Spoon the cheesecake filling evenly over the partially baked brownie layer in each muffin liner. Bake for 15-18 minutes, or until the centers are almost set.

Turn off the oven and let the cheesecakes cool in the oven with the door slightly ajar for 1 hour. Remove and cool completely on a wire rack. Transfer to the refrigerator and chill for at least 4 hours, or overnight, before serving.