Preheat the oven to 350°F (175°C) and prepare a baking pan.
Melt butter in a medium saucepan over low heat.
Mix in granulated sugar and vanilla extract until well combined.
Remove from heat and allow to cool slightly before adding eggs.
Add eggs one at a time, stirring well after each addition.
Sift together flour, cocoa powder, and salt; fold into the mixture.
Set aside the brownie batter and prepare the cheesecake layer.
In a separate bowl, beat softened cream cheese, powdered sugar, and 1 egg until smooth.
Pour half of the brownie batter into the prepared pan, followed by the cheesecake mixture, then top with the remaining brownie batter.
Use a knife or skewer to gently swirl the batters together.
Bake in the preheated oven for 30-35 minutes or until a toothpick inserted in the center comes out with a few moist crumbs.
Allow the brownies to cool completely in the pan, then cut into squares.
