Adjust an oven rack to the lower-middle position and preheat oven to 325 degrees F. Butter an 8-inch square baking pan. Fold two 16-inch pieces of foil lengthwise to measure 8 inches wide. Fit 1 seet in the bottom of the greased pan, pushing it into the corners and up the sides of the pan (the overhang will help in removal of the baked brownies). Fit the second sheet in the pan the same way, perpendicular to the first. Butter the foil; set aside.
Whisk the flour, salt and baking powder together in a small bowl; set aside.
In a medium bowl, combine the chocolate and butter. Microwave in 30-second increments at 50% power, stirring after each, until completely melted and smooth. Whisk in the sugar and vanilla extract; allow the mixture to cool slightly. Whisk in the eggs, one at a time, fully incorporating each before adding the next. Continue whisking until the mixture is completely smooth. Add the dry ingredients and whisk until just incorporated.
Make the cream cheese filling by beating the cream cheese, sugar, vanilla and egg yolk together in a small bowl until evenly blended.
Pour half the brownie batter into the prepared pan, spreading it in an even layer. drop half the cream cheese mixture, by spoonfuls, over the batter. Repeat, layering the remaining brownie batter and cream cheese filling. Use a butter knife to gently swirl the brownie batter and cream cheese filling, creating a marbled effect.
Bake until the edges of the brownies have puffed slightly, the center feels not quite firm when touched lightly, and a toothpick or cake tester inserted into the center comes out with several moist, fudgy crumbs adhering to it, 50 to 60 minutes.
Cool the brownies in a pan on a wire rack for 5 minutes. Remove the brownies from the pan using the foil handles. Place the brownies on a wire rack; allow them to cool to room temperature. Refrigerate until chilled, at least 3 hours. Cut into squares and serve. The brownies can be stored in an airtight container in the refrigerate for up to 5 days.