Preheat your oven to 350 degrees Fahrenheit. Grease and line a 9×13 inch baking pan with parchment paper, leaving an overhang on the sides.
In a large bowl, mix the melted butter and 2 cups of sugar until combined.
Beat in the 4 eggs one at a time, then 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 and mix until just combined. Do not overmix.
Pour about two-thirds of the brownie batter into the prepared pan and spread evenly.
In a medium bowl, beat the softened cream cheese, 1/4 cup sugar, 1 egg, and 1/2 teaspoon vanilla extract until smooth.
Drop spoonfuls of the cream cheese mixture over the brownie batter in the pan.
Pour the remaining one-third of the brownie batter over the cream cheese layer.
Use a knife or skewer to gently swirl the layers together to create a marbled effect.
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 out using the parchment paper overhang and cutting into squares.
Notes
For the best swirl, ensure your cream cheese mixture is smooth before layering.
Cool the brownies completely before cutting for clean slices.
You can chill the brownies for 30 minutes before slicing for firmer texture.