Preheat oven to 350°F and grease a 9-inch square or springform pan. Set aside.
For the dough:
In a large bowl, mix together the flour, baking powder, and cocoa powder with an electric mixer until thoroughly combined. Add sugar, vanilla, eggs, and butter and mix on low at first. Then, increase speed to high until dough is smooth.
Knead the dough in the bowl a bit, and press 2/3 of the dough into the prepared pan, making sure it goes at least an inch up the sides.
For the filling:
Mix together the butter, cream cheese, sugar, vanilla extract, eggs, and cornstarch with an electric mixer. Pour into the springform pan.
Make small lumps from the remaining chocolate dough and drop them evenly across the top of the cake. Bake until cake is set and golden yellow, about 50-60 minutes. Allow to cool before serving. Enjoy!