In a medium bowl, sift together the flour and Cocoa powder and set aside.
In a medium microwave-proof bowl, melt the butter in the microwave for about 1 minute. Immediately add the chopped chocolate and stir until melted and smooth. If bits of chocolate remain, place the mixture back in the microwave for 10 seconds.
In the bowl of an electric mixer, beat the eggs, granulated sugar, light brown sugar, pure vanilla extract, Irish Cream, and salt on medium speed until smooth. Add the melted chocolate mixture and beat until well incorporated. Add the flour mixture and mix on low until just combined. Do not overmix!
Spread the brownie batter in the prepared pan. Using a spoon, dollop the cheesecake batter over the cheesecake layer, about 8 dollops (for the perfect Irish Cream Cheesecake Marbled Brownie, leave as much space as possible between the dollops).
Using a wooden skewer, swirl the cheesecake batter through the Brownie batter, making a marbled pattern. (Don't overdo the marbling, or the batters will get muddled).
Bake the Cheesecake Marbled Brownies until puffed and set in the center, 40-45 minutes. Let it cool completely in the pan on a wire rack. Cut the Cheesecake Marbled Brownies into 3 inches square pieces. Enjoy!