Step 1

Position a rack in the middle of the oven and preheat the oven to 325 degrees F. Line a 9-by 13- inch baking pan with foil, leaving a 2-inch overhang on at least 2 sides. Butter the foil.

Step 2

Whisk together the cocoa powder, salt and 1 1/2 cups of the flour in a medium bowl.

Step 3

Melt the butter and chocolate, stirring frequently, in a medium saucepan over medium heat. Transfer to a bowl and let cool for 10 minutes. Whisk in 2 cups of the sugar and 4 of the eggs. Add the flour mixture, and stir to combine. Chill for 10 minutes.

Step 4

Meanwhile, beat together the cream cheese, vanilla extract, remaining 1/3 cup sugar and 1 egg with an electric mixer in a large bowl on medium-high speed. Add the remaining 1/4 cup flour and beat until just combined.

Step 5

Use 2 ice cream scoops or large spoons to drop alternating scoopfuls of the 2 batters into the prepared pan. (You will have more brownie batter than cheesecake batter and that's okay; just make sure to disperse the batters as evenly as possible.) Spread a couple of kitchen towels on your countertop. Gently drop the baking pan onto the countertop a few times until the batter evens out (the towels should catch the splatters).

Step 6

Make the swirls: Drag a long wooden skewer through the batter, making sure the skewer reaches down to the bottom of the pan. This will marble the colors in a tie-dye effect. Tap the baking pan on the towels a few more times to smooth out the batter.

Step 7

Bake the brownies, rotating about halfway through, until the top is set and the skewer inserted in the center of the brownies comes out with only a few moist crumbs, about 50 minutes.

Step 8

Let the brownies cool completely in the pan set on a rack. Use the foil overhang to help lift them out of the pan. Cut into 16 pieces. Store in an airtight container at room temperature for up to 3 days.