Preheat oven to 350°F (175°C). Line a 9-inch square baking pan with parchment paper so that the paper overhangs by about 2 inches on opposite sides. Spray the paper with nonstick baking spray.
Place the chocolate and butter in a microwave-safe bowl. Heat in the microwave at half-power in 30-second increments until the butter has melted and the chocolate melts when stirred. Stir until smooth. Set aside to cool slightly.
Combine the sugar, brown sugar, eggs, vanilla, and salt in a large bowl. Add the cooled chocolate, and mix until combined.
Add the flour, and mix just until combined.
Transfer the batter to the prepared pan, and spread evenly. Set aside.
To make the cheesecake swirl:
Using an electric mixer on medium speed, beat the cream cheese, sugar, vanilla, and egg until thoroughly combined and smooth. Add the cookie butter and mix until combined.
Drop the cheesecake mixture by small amounts over the top of the brownie batter. Use an offset spatula or thin knife to swirl into the brownie batter.
Bake 40 to 45 minutes, or until a pick inserted into the center comes out clean.
Cool the brownies completely in the pan on a wire rack. Then cover and refrigerate at least 4 hours before cutting into bars.
To cut into bars, use the overhanging parchment paper to transfer the brownies to a cutting board. Use a sharp knife to cut into bars.
Notes
*Lightly beat the egg, and measure half of that volume to use in the recipe. That's usually about 1 & 1/2 tablespoons.
**Look for cookie butter alongside other spreads like peanut butter and Nutella.
Store in an airtight container in the refrigerator up to 5 days.