Preheat your oven to 325°F (160°C) and line a muffin tin with paper liners.
In a mixing bowl, combine the brownie mix, vegetable oil, egg, and water. Stir until well combined.
Divide the brownie batter evenly among the muffin cups, filling each about halfway.
Bake the brownie bases for 10 minutes, then remove from the oven and let cool slightly.
In another bowl, beat the softened cream cheese until smooth. Add the sugar, vanilla extract, and egg, mixing until well combined.
Stir in the sour cream and chocolate chips, if using, until just combined.
Spoon the cheesecake mixture over the cooled brownie bases, filling each cup almost to the top.
Bake for an additional 15-18 minutes, or until the cheesecakes are set but still slightly jiggly in the center.
Allow the mini cheesecakes to cool at room temperature, then refrigerate for at least 2 hours before serving.