Preheat the oven to 350°F/ 175°C and line an 8x8 baking pan with aluminum foil.
Whisk together all of the cheesecake ingredients in a small or medium bowl and set aside.
In a medium bowl, whisk together the flour and salt. Set aside.
Melt the butter, you can do this either in the microwave using a microwave-safe bowl or over a double boiler. Once the butter is melted, either in the microwave or over the stove, add your chopped chocolate. Let the chocolate sit for a few minutes and then stir until it is completely melted. If the chocolate still hasn't melted, place the bowl back in the microwave and melt in 15 second increments. Allow the mixture to cool while you work on the next step.
In a stand mixer fitted with the whisk attachment, or in a large bowl with a hand mixer, whisk the oil, sugar, light brown sugar, eggs, egg yolk and vanilla extract for 6 minutes on medium-high speed.
Add your cocoa powder to the melted chocolate and fold until it is completely smooth.
Pour the sugar mixture into the melted chocolate butter mixture and use a rubber spatula to fold everything together. Pour in the flour mixture and fold until there are no more streaks of flour.
Pour ⅔ of the batter into the prepared pan, keeping just less than 1 cup of batter to the side. Add 1 ⅕ tablespoon water to the remaining brownie batter and mix. Spread the cream cheese mixture on top until it covers the surface, then dollop the reserved brownie mixture on. Use a butter knife to create the swirls.
Bake for 30-33 minutes. Allow the brownies to cool completely before slicing, or they'll fall apart! Cut into 9 squares or 16 mini brownies.
Notes
Room Temperature: I make sure that all of my ingredients are at room temperature before I start the recipe, so pull out all of the ingredients about 2 hours before you start baking.
Salt: If you don’t have kosher salt, halve the amount of salt called for in the recipe. 1 teaspoon kosher salt = ½ teaspoon fine salt.
Butter: I use European style butter, like Kerry Gold, in my recipes. This will make your finished bake much creamier and richer.
Storage: keep in an airtight container in the fridge for up to 5 days. You can freeze the bars for up to 3 months. Let them defrost in the fridge overnight before eating.