Bownie with cream cheese swirl

ingredients 
  10 tablespoons unsalted butter, cut into pieces, plus more for pan
1 cup plus two tablespoons all-purpose flour
1/4 cup unsweetened cocoa powder
1/2 teaspoon baking powder
1/2 teaspoon salt
8 ounces semisweet or bittersweet chocolate, chopped
4 ounces room-temperature bar cream cheese
1 1/2 cups sugar
4 large eggs 

Preheat oven to 350 degrees. Brush a 9-inch square baking pan with
butter. Line bottom and two sides with a strip of parchment paper,
leaving a 2-inch overhang on the two sides. Butter paper, and set pan
aside. In a small bowl, whisk flour, cocoa, baking powder, and salt;
set aside. 
Place 8 tablespoons (1 stick) butter and chocolate in a large
heat-proof bowl set over (not in) a saucepan of gently simmering
water. Heat, stirring occasionally, until smooth, 2 to 3 minutes;
remove bowl from pan. Add 1 1/4 cups sugar; mix to combine. Add 3
eggs, and mix to combine. Add 1 cup all-purpose flour; mix just until
moistened (do not over mix). 
Prepare cream-cheese mixture: Whisk bar cream cheese with 2
tablespoons room-temperature butter. Whisk in 1/4 cup sugar, 1 egg,
and 2 tablespoons all-purpose flour. Alternately spoon chocolate
batter and cream-cheese mixture into pan; with the tip of a paring
knife, swirl to marble. 
Transfer batter to prepared pan; smooth top. Bake until a toothpick
inserted in center comes out with a few moist crumbs attached, 50 to
60 minutes. Cool in pan for 30 minutes. Using paper overhang, lift
brownies out of pan; transfer to a rack to cool completely (still on
paper). On a cutting board, using a dampened serrated knife, cut into
16 squares. Store in an airtight container at room temperature, up to
2 days.