Using a stand or hand mixer, whip the cream cheese until it is fluffy, 1-2 minutes on high.
Melt the chocolate using either a double boiler or a microwave. If using a microwave with high wattage, cook only 10-15 seconds at a time, stirring in between, until the chocolate is just melted.
After the chocolate has cooled a little, add it to the cream cheese and mix until it is fully combined and fluffy, 2-3 minutes.
Add the eggs one at a time, mixing until each one is fully combined.
Spoon the cheesecake batter over the brownie layer. Then, using a table knife, dip down through the batter and swirl upwards, like using a rowing oar. This should create a swirl pattern. Alternatively, you can layer reserved brownie batter on top of the cheesecake and then use a knife or toothpick to create swirls.
Cover the pan with aluminum foil. Bake at 350° F (180° C) for 60-70 minutes, until a chopstick or toothpick inserted in the center comes out mostly clean.