First, preheat oven to 350 degrees Fahrenheit. Line a springform pan with parchment paper.
Make the brownie batter. Add melted butter and 1 cup dark chocolate chips to a bowl. Stir until creamy and fully melted. If needed, microwave for 10 to 15 seconds. Set aside.
In a mixing bowl, add eggs and sugar. Whisk vigorously for 2 to 3 minutes, until light and frothy.
Add the melted chocolate mixture to the mixing bowl. Stir to combine.
Then, add in dark cocoa powder, vanilla, flour and espresso powder. Stir to combine.
Fold in extra chocolate chips if desired.
Pour ¾ of the batter into the lined pan. Smooth out into one even layer. Reserve the remaining batter to swirl into the cheesecake filling.
Then, make the cheesecake filling. In a large mixing bowl or the bowl of a stand mixer, add the cream cheese, Greek yogurt, vanilla, sugar and flour. Use an electric mixer to beat until fully creamy.
Then, add in the two eggs. Mix until just combined. Do not over mix.
Pour the cheesecake filling on top of the brownie batter. Then, add the remaining brownie batter. Swirl together.
Bake for 45 to 50 minutes, or until the cheesecake is slightly jiggly in the middle. Turn the oven off and slightly open the oven door.
Allow the cheesecake to cool down in the oven for 2 hours with the door slightly ajar.
Finally, remove from the oven. Cool at room temperature for 4 hours then place covered in the fridge overnight.
Lastly, remove from the fridge and serve!