Preheat the oven to 350 °F (175 °C). Line a 9-inch square baking pan with parchment paper or grease it with butter or nonstick cooking spray. Set aside.

In a small bowl, microwave the cream cheese until soft, about 20 seconds. In the bowl of an electric mixer, beat the softened cream cheese with the sugar, egg yolk, vanilla extract, Irish Cream, and flour until smooth. Set aside.

Sift the flour and cocoa powder into a medium bowl and set aside.

In a medium microwave-safe 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 in the microwave for 10 seconds.

In the bowl of an electric mixer, beat the eggs, granulated sugar, light brown sugar, 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 brownie layer, about eight dollops. Leave as much space as possible between the dollops. Using a wooden skewer, swirl the cheesecake batter through the brownie batter to create a marbled pattern. Do not overdo the marbling, or the batters will become muddled.

Bake the Cheesecake Brownies until puffed and set in the center, about 40-45 minutes. Let cool completely in the pan on a wire rack.

Cut the Cheesecake Brownies into 3-inch square pieces.