For the Brownie: Preheat oven to 350ºF. Line an 8-inch by 8-inch baking pan with foil, leaving enough hanging over the two opposite sides to use as handles. Coat the foil with cooking spray.
Combine the unsweetened chocolate, semisweet chocolate, and butter in a microwaveable bowl. Microwave on 50 percent of the power just until the chocolate is soft enough to stir smooth, 2 to 3 minutes, stopping to stir every minute.
In a medium bowl, whisk together the sugar, eggs, vanilla, and salt. Whisk in the chocolate mixture. With a rubber spatula, stir in the flour just until blended. Remove 1/2 cup brownie batter to a small bowl. Spread the remaining batter evenly in a prepared baking pan.
For the Cheesecake Topping: Using an electric mixer on medium speed, beat the cream cheese until smooth, 1 minute. Beat in the sugar and vanilla until smooth, about 1 minute. Beat in the egg for 30 seconds.
Pour the topping evenly over the brownie batter. Drop the reserved brownie batter in small dollops over the topping. Use a dinnerware knife to swirl together the topping and brownie batter to create a marbled effect.
Bake until a toothpick inserted in the center comes out slightly wet, 35 to 40 minutes. Transfer to a rack to cool. When cool, use the foil to lift the entire cake of brownies from the pan. Cut into squares.
Tip: If you can’t find Reduced-Fat New York-Style Cheesecake Cream Cheese Spread from Panera Bread (it's available seasonally), replace it with any reduced-fat cream cheese and increase the amount of sugar in the topping to 1/3 cup.