Preheat the oven to 350°F. Butter a 9-inch-square metal baking pan.
Melt the butter in a saucepan. Off the heat, stir in sugar, then the cream cheese, followed by the eggs and vanilla. Slowly stir in the flour, cocoa, baking powder and salt, until the batter is smooth and free of lumps.
Spread the batter into the prepared pan. Bake until a toothpick or a skewer inserted ¾ inch into the center of the brownies comes out with just a few moist clumps clinging to it, about 40 minutes. Let the brownies cool completely in the pan on a rack.
Cut into squares. Store the brownies, covered, in the refrigerator.