1FOR THE CREAM CHEESE FILLING: Microwave cream cheese until soft, 20 to 30 seconds.
2Add sour cream, sugar, and flour and whisk to combine. Set aside.
3Adjust oven rack to middle position and heat oven to 325 degrees.
4Make foil sling for 8-inch square baking pan by folding 2 long sheets of aluminum foil so each is 8 inches wide. Lay sheets of foil in pan perpendicular to each other, with extra foil hanging over edges of pan. Push foil into corners and up sides of pan, smoothing foil flush to pan. Grease foil.
5FOR THE BROWNIE BATTER: Whisk flour, baking powder, and salt together in bowl and set aside.
6Microwave chocolate and butter in bowl at 50 percent power, stirring occasionally, until melted, 1 to 2 minutes.
7Whisk sugar, eggs, and vanilla together in medium bowl.
8Add melted chocolate mixture (do not clean bowl) and whisk until incorporated.
9Add flour mixture and fold to combine.
10Transfer 1/2 cup batter to bowl used to melt chocolate.
11Spread remaining batter in prepared pan.
12Spread cream cheese filling evenly over batter.
13Microwave bowl of reserved batter until warm and pourable, 10 to 20 seconds.
14Using spoon, dollop softened batter over cream cheese filling, 6 to 8 dollops.
15Using knife, swirl batter through cream cheese filling, making marbled pattern, 10 to 12 strokes, leaving 1/2-inch border around edges.
16Bake until toothpick inserted in center comes out with few moist crumbs attached, 35 to 40 minutes, rotating pan halfway through baking.
17Let cool in pan on wire rack for 1 hour.
18Using foil overhang, lift brownies out of pan. Return brownies to wire rack and let cool completely, about 1 hour. Cut into 2-inch squares and serve.