Preheat the oven to 325°F (163°C). Line 10 cups of a standard 12-cup muffin tin with paper liners.
In a medium mixing bowl, whisk together the melted butter and 1/2 cup sugar until well combined.
Add one egg and 1/2 teaspoon vanilla extract to the butter mixture, whisking until the batter is smooth and slightly glossy.
Sift the flour, cocoa powder, and salt into the wet ingredients. Fold gently with a spatula until no dry streaks remain.
Distribute the brownie batter evenly among the 10 lined muffin cups (approximately 1.5 tablespoons per cup).
Bake the brownie bases for 10 minutes. Remove the tin from the oven but keep the oven temperature at 325°F.
While the brownies are par-baking, prepare the cheesecake filling: In a separate bowl, beat the softened cream cheese and 1/4 cup sugar until completely smooth and aerated.
Incorporate the second egg, sour cream, and 1/2 teaspoon vanilla extract. Mix on low speed until just combined to avoid incorporating excess air.
Spoon the cheesecake mixture over the warm brownie bases, filling each liner nearly to the top.
Return the tin to the oven and bake for 18 to 20 minutes, or until the edges of the cheesecake are set but the centers maintain a slight jiggle.
Allow the cheesecakes to cool in the tin at room temperature for 30 minutes, then transfer to the refrigerator to chill for at least 4 hours before serving.