Preheat oven to 325°F (170°C). Spray an 8-inch square baking pan with cooking spray. Line pan with parchment paper, letting excess extend over sides of pan.

In the top of a double boiler, combine chocolate and butter. Cook over simmering water, stirring occasionally, until melted and smooth. Turn off heat, and whisk in sugars until well combined. (Mixture will not be completely smooth.) Remove from heat, and let cool slightly, 3 to 5 minutes.

In a medium bowl, whisk together flour, cocoa, salt, and espresso powder.

Slowly add eggs to chocolate mixture, whisking until combined. Whisk in vanilla. Fold in flour mixture just until combined. Spread two-thirds of batter (about 2⅔ cups [about 760 grams]) in prepared pan. Spoon Cheesecake Layer on top of batter, smoothing flat with an offset spatula. Spoon remaining batter in large dollops (about 48 grams each) on top of Cheesecake Layer. Using a wooden pick, swirl layers together.

Bake until brownie on top is shiny, center is set, and a wooden pick inserted in brownie comes out with a few moist crumbs, 55 minutes to 1 hour and 5 minutes, covering edges with foil after 40 minutes of baking to prevent excess browning. Let cool in pan for 15 minutes. Using excess parchment as handles, remove from pan, and let cool completely on a wire rack before cutting into bars. Refrigerate in an airtight container for up to 6 days. Let come to room temperature before serving.