Preheat oven to 350°F. Line a 9x9-inch square pan with foil and spray with nonstick cooking spray.
Make the brownies
Place chocolate and butter in a large microwave-safe bowl. Heat on high power in 30 second increments, stirring between each, until chocolate and butter are melted and smooth (about 2 minutes, depending on your microwave).
Stir sugar and cocoa into chocolate and butter mixture using a spatula or wooden spoon. Stir in 3 eggs and vanilla, then stir in salt. Mixture will be grainy looking but smooth. Stir in flour carefully.
Spread brownies in prepared pan and set aside.
Make the cheesecake
Beat cream cheese with sour cream until smooth, then beat in 2 eggs, sugar and vanilla.
Pour mixture over the top of the brownies in pan. Use a butter knife or a long skewer to swirl the brownies.
Bake for 50-55 minutes, or until slightly puffed and no longer glossy (will be light golden around the edges of the foil). Cool completely at room temperature then chill for at least 4 hours before slicing and serving.
Store in an airtight container for up to 3 days in the refrigerator or freeze for up to 3 months.
Notes
It’s very important that your cream cheese, sour cream, and eggs are room temperature before you make the cheesecake mixture to avoid lumps.