Preheat your oven to 350°F (175°C). Grease and line an 8x8 inch baking dish with parchment paper, leaving some overhang for easy removal later.
In a saucepan over low heat, melt the unsalted butter completely. Remove from heat and stir in granulated sugar until well combined.
Add in the eggs, one at a time, stirring vigorously after each addition. Mix in 1 teaspoon of vanilla extract.
In a separate bowl, whisk together the flour, cocoa powder, salt, and baking powder. Gradually add this dry mixture to the butter mixture, stirring until just combined. Do not overmix.
In another bowl, beat together the softened cream cheese, powdered sugar, egg yolk, and 1/2 teaspoon vanilla extract until smooth and creamy.
Pour about two-thirds of the brownie batter into the prepared baking dish and spread it evenly.
Spoon dollops of the cream cheese mixture over the brownie batter. Use the remaining brownie batter to add dollops on top of the cream cheese mixture.
Using a skewer or a knife, gently swirl the cream cheese and brownie batter together to create a marbled effect. Be careful not to over-swirl to keep distinct layers.
Bake the brownies in the preheated oven for 25-30 minutes, or until a toothpick inserted into the center comes out mostly clean (slight moist crumbs are okay).
Once done, remove from oven and allow to cool completely in the baking dish before lifting out using the parchment overhang. Cut into squares.
Notes
Serve on a rustic wooden platter or a colorful cake stand, dusted with powdered sugar. Pair with vanilla ice cream for a delightful contrast!