In a large bowl, whisk together the eggs, sugars, oil, vanilla, salt, and baking powder. Set aside.
In a small saucepan on low heat, melt the chocolate and butter together, stirring often to prevent burning. Stir over low heat until completely smooth. Remove from the heat and whisk in the cocoa powder.
Add the chocolate mixture to the egg mixture and stir until completely smooth.
Add the flour and stif just until combined.
Pour about ⅔ of the brownie mixture on top of the baked crust. Smooth the mixture with a spatula or an offset spatula.
Carefully pour the cheesecake mixture over the brownie batter. Drop spoonfuls of the remaining brownie batter on top of the cheesecake. Pull a knife or offset spatula through the brownie dollops to create swirls. Be careful not to push down too deep and break the crust.
Bake for 35 to 45 minutes. The edges should be set, and there should be a slight giggle in the center. Remove from the oven and cool on a wire rack for an hour. Transfer to the refrigerator and chill for at least 4 hours or overnight.
Use the parchment sling to remove the Cheesecake Brownie Bars from the pan. Use a sharp knife to cut into 12 large squares or 24 small squares. Wipe the knife on a damp towel after each cut to make sure that slices cut cleanly.