Preheat the oven to 350°F (175°C).
Line an 8×8 glass baking dish with parchment paper. (You can also spray your pan with cooking spray to help avoid sticking, but personally, I never do.) Set aside.
In a mixing bowl, combine the flour, salt, and cocoa powder. Set aside.
In a small saucepan over medium heat, melt the chopped chocolate and unsalted butter, stirring often until completely melted and shiny. Remove from the heat.
In a large bowl, beat together the sugar, eggs, and egg yolk (from the brownie ingredients) until the mixture is pale yellow. Add the oil and vanilla extract and mix again.
Pour the melted chocolate mixture into the sugar mixture and mix well.
Add the flour mixture to the bowl 1/3 at a time, stirring with a wooden spoon or rubber spatula between each addition. Once fully incorporated, scrape down the sides of the bowl and mix again.
Spoon the brownie batter into your prepared pan. Place it in the oven and bake for 20–25 minutes, or just until a crust forms on the top of the brownies. (Tip: Look for a slight color change and a shiny top. You can also gently touch the surface—there shouldn’t be any batter on your finger.)
Remove the brownies from the oven and let them cool for 5–7 minutes while you prepare the cream cheese mixture.
In a large bowl, combine all the cheesecake ingredients and beat until smooth and creamy.
Spoon the cheesecake mixture on top of the brownies and gently smooth it out with a rubber spatula, doing your best to create one even layer.
Return the pan to the oven and bake for 25–30 minutes, or until the cheesecake layer is set. The center should be slightly jiggly but firm to the touch.
Once done, remove from the oven and let the brownies cool to room temperature.
Then cover the pan with plastic wrap and place it in the fridge to chill for 2–4 hours, or overnight.
Once chilled, remove the brownies from the pan and the parchment paper. Drizzle with melted chocolate (if using), and cut into 16 pieces.
Serve and enjoy!