1. Place a rack in the center of the oven and preheat oven to 350 degrees. Spray a 9-inch square baking pan with cooking spray, dust with flour, and tap out the excess; place the pan on a large baking sheet and set aside.

Brownies:

1. Place flour, baking powder, and salt in a small mixing bowl and whisk to combine.
2. Place the butter and chocolate in a heatproof bowl set over simmering water. Stir until the butter and chocolate are just melted then remove from the heat. Allow to cool for a few minutes.
3. Whisk sugar into chocolate mixture, then add the eggs one at a time, mixing well after each addition. Whisk in the vanilla and espresso powder, then fold in the dry ingredients with a rubber spatula until the flour is just incorporated. Set aside.

Cheesecake:

1. Stir the espresso powder into the boiling water; allow to cool for a few minutes. Place the cream cheese in the bowl of a stand mixer fitted with the paddle attachment and beat on medium until very smooth. Add the sugar and beat for several minutes more. Beat in the vanilla and espresso mixture, then add the eggs 1 at a time, beating for 1 minute after each addition. Turn speed to low and add the sour cream and flour.
2. Stir the brownie batter with a rubber spatula several times, then pour 3/4 of it into the prepared pan—you’ll have enough just to cover the bottom of the pan. Smooth the top. Pour the cheesecake mixture onto the brownie mixture in an even layer. Dot the cheesecake with the remaining brownie batter; use a knife to swirl the cheesecake and top brownie layer.
3. Bake for 30 to 45 minutes, until the brownies pull away from the sides of the pan and the cheesecake layer is puffed up. Cool to room temperature on a wire rack then refrigerate for 2 hours, until completely chilled. Slice into bars and serve.