Preheat your oven to 350℉/176℃/Gas Mark 4.
Melt the unsalted butter with the dark chocolate chips in either a saucepan on low heat or in the microwave. If using the microwave, heat in 30-second intervals, stirring between each interval. If melting in a saucepan, continuously stir to avoid the chocolate from burning.
Once the butter and chocolate chips have melted completely, whisk the cocoa powder into the chocolate mixture. Set aside.
In a large bowl, beat the granulated sugar, brown sugar, and eggs together until it is a light, fluffy mixture. Beat for approximately 2 minutes, scraping down the sides as needed.
Pour the chocolate mixture into the egg mixture and beat on low speed until fully incorporated.
Add the salt, vanilla extract, and all-purpose flour, and beat slowly until just incorporated together and there are no flour lumps seen.
Pour two-thirds of the mixture into a parchment paper-lined 8x8 dish.
Slowly dollop the cream cheese filling on top of the brownie mixture in the dish.
Once the cream cheese filling is placed on top of the brownie batter, take the rest of the brownie batter and place it on top of the cream cheese. Next, take a knife and swirl it through the brownie and cream cheese, swirling as much as you desire.
Bake for 50 minutes to 1 hour or until a knife inserted into the centre comes out mostly clean. A few crumbs on the knife in brownies is desired.
Remove from the oven and let cool in the pan for 10 minutes.
Remove from the pan and continue to let cool for 2 hours until completely cool.
Cut up into squares and enjoy!