Preheat oven to 350°F (175°C). Line 24 mini muffin pans with paper liners. (Or grease the cups if not using liners.)
Place the butter and chocolate in a microwave-safe bowl. Heat at half-power in 30-second increments until the butter melts and the chocolate melts when stirred. Stir well. Set aside to cool slightly.
Combine the sugar, egg, and vanilla. Stir in the cooled chocolate mixture. Add the flour and salt, and stir just until combined.
Divide the batter evenly among the muffin cups, using about 2 teaspoons per cup.
Bake 6 to 8 minutes, or until slightly set. Set aside.
To make the cheesecake filling:
Using an electric mixer on medium speed, beat the cream cheese, sugar, egg, and vanilla until smooth. Mix in the sour cream.
Divide the cheesecake batter evenly among the muffin cups, using about a scant tablespoonful per cup.
Bake 12 to 15 minutes, or until the cheesecakes are set.
Cool in the pan on a wire rack. Then refrigerate at least 2 hours before serving.
If desired, top with sweetened whipped cream and other garnishes before serving. Keep refrigerated.
Notes
Store in an airtight container in the refrigerator up to 4 days.