Preheat oven to 325F (162C). Line an 6" square pan with parchment paper with the ends hanging over both sides of the pan. This creates handles to remove the cooked brownies from the pan.

Place the chocolate and butter in a medium microwave safe bowl. Microwave for 30 seconds, then stir the mixture. Continue microwaving and stirring in 10 second intervals until the chocolate is fully melted and the mixture is smooth. Whisk in the sugar until smooth. Let the mixture cool slightly. Once the chocolate mixture is slightly cooled, whisk in the egg until well incorporated. Mix in the Baileys Irish Cream.

In a small bowl, whisk together the flour, baking powder, and salt. Add the flour mixture to the chocolate mixture and stir until just combined. Reserve about 1/6 cup brownie batter and transfer rest to the parchment-lined baking dish and smooth to the edge. Place in refrigerator to chill while whipping up the cheesecake.

In a medium bowl, beat the cream cheese, sugar, egg, and Baileys Irish Cream until very smooth. Try not to over beat. Spoon the cheesecake mixture in large dollops on top of the brownie batter. Smoothen it with a spatula.

Mix the reserved brownie batter with a tablespoon of water and mix together. You’re basically thinning the batter so it’s easier to mix in. Add more water as needed until the batter is more the consistency of cake batter. Dot the top of the cheesecake with spoonfuls of the thinned batter. Use a skewer to swirl the brownie batter around.

Bake for 32-35 minutes, until the edges look slightly golden brown and the center is not quite firm when touched lightly, but is set. Cool the brownies completely in the pan, then remove using the parchment handles. Wait until they are complete cooled to cut.