Preheat your oven to 350°F (175°C) and grease a 9x13-inch baking pan.
In a medium saucepan, melt the butter over low heat.
Once melted, remove from heat and stir in the granulated sugar until well combined.
Add the eggs, one at a time, mixing well after each addition.
Stir in the vanilla extract.
In a separate bowl, whisk together the flour, cocoa powder, and salt.
Gradually add the dry ingredients to the wet mixture, stirring until just combined.
In another bowl, beat the cream cheese until smooth, then add powdered sugar and milk, mixing until creamy.
Spread half of the brownie batter into the prepared pan, followed by dollops of cream cheese mixture.
Top with the remaining brownie batter and swirl with a knife for a marbled effect.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted comes out clean.
Allow to cool before cutting into squares and serving.