Preheat your oven to 350°F (175°C). Line a 9×13 inch baking pan with parchment paper, leaving an overhang on the sides for easy removal. Lightly grease the paper.
In a large bowl, whisk together the melted butter and 2 cups of sugar until combined.
Beat in the 4 eggs one at a time, mixing well after each addition. Stir in 1 teaspoon of vanilla extract.
In a separate bowl, whisk together the flour, cocoa powder, salt, and baking powder. Gradually add the dry ingredients to the wet ingredients, mixing only until just combined. Do not overmix.
Spread the brownie batter evenly into the prepared baking pan.
In a medium bowl, beat the softened cream cheese until smooth. Add the 1/4 cup of sugar, the remaining egg, and 1/2 teaspoon of vanilla extract. Beat until the mixture is smooth and creamy.
Drop spoonfuls of the cream cheese mixture over the brownie batter.
Use a knife or a skewer to gently swirl the cream cheese mixture into the brownie batter to create a marble pattern. Do not over-swirl.
Bake for 30 to 35 minutes, or until a toothpick inserted near the center comes out with moist crumbs attached, not wet batter.
Let the brownies cool completely in the pan on a wire rack before lifting them out using the parchment paper overhang. Cut into squares.
Notes
For a simpler version, you can use one box of your favorite fudgy brownie mix and follow the box directions for the base, then prepare and swirl the cream cheese topping as directed above.
For extra fudgy brownies, reduce the baking time by 2-3 minutes.
Chill the brownies for at least one hour before cutting for cleaner slices.