Preheat your oven to 325°F (160°C).
Grease your 9-inch springform pan lightly with butter or cooking spray and set it aside.
In a large mixing bowl, add the room-temperature cream cheese. Using an electric mixer, beat until smooth and creamy, about 2-3 minutes.
Gradually add the sugar and flour to the cream cheese mixture. Beat until well combined and fluffy.
Add the mascarpone cheese to the mixture and continue to beat until fully combined.
Add the eggs one at a time, mixing well after each addition. Then, stir in the vanilla extract.
Gently fold in the sour cream using a rubber spatula.
Pour the warm, melted chocolate into the mixture and gently fold until fully incorporated.
Pour the cheesecake batter into the prepared springform pan. Place the pan on a baking sheet and bake for 55-65 minutes.
Once baked, turn off the oven and crack the door open. Let the cheesecake cool in the oven for about an hour, then chill in the refrigerator for at least 4 hours.
When ready to serve, carefully remove the sides of the springform pan. Slice the cheesecake and serve chilled.