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.