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 1 cup 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 3eggs, and mix to combine. Add flour and cocoa mixture; mix just until moistened (do not overmix).

Prepare cream-cheese mixture: Whisk 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.

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.

Lift brownies out of pan; transfer to a rack to cool completely. On a cutting board, using a dampened serrated knife, cut into 16 squares.