Preheat your oven to 350° F. Grease an 9x9" pan (if you want less thick brownies, use a 9x13" pan).
Make the brownies: In a medium bowl, beat the eggs with the cocoa powder, salt, baking powder, espresso powder (if using), and vanilla. Beat for a few minutes until well combined.
In the microwave or in a saucepan over medium heat, melt the butter with the sugar and stir until the sugar dissolves. Add the hot sugar and butter mixture to the bowl with the cocoa mixture. Stir to combine well. Add the flour and chocolate chips and mix well until shiny.
Pour the brownie batter into the prepared pan and bake for 20 to 25 minutes—the crust should be just set, but the brownies shouldn't be cooked through.
While the brownies bake, make the cheesecake layer. In a large bowl or stand mixer, beat together the cream cheese, softened butter, and cornstarch. Slowly add the condensed milk, egg, and vanilla and mix until very well combined.
When the brownies have finished their first bake, remove them from the oven and pour the cheesecake batter over the top. Return the pan to the oven and bake for 25 to 30 minutes, or until the top is just beginning to brown. Let cool, then slice.