Preheat the oven to 325°F (163°C) and line a muffin tin with paper liners.
In a medium bowl, combine the brownie mix, vegetable oil, and 1 egg. Stir until well blended.
Divide the brownie batter evenly among the muffin cups, filling each about 1/3 full. Bake for 10 minutes, then remove from the oven and let cool slightly.
In a large mixing bowl, beat the softened cream cheese until smooth. Add the granulated sugar and vanilla extract, mixing until well combined.
Add 2 eggs, sour cream, flour, and salt to the cream cheese mixture. Beat until smooth and creamy.
If using, fold in the chocolate chips gently.
Pour the cheesecake batter over the brownie layer in each muffin cup, filling them about 3/4 full.
Bake for an additional 20-25 minutes, or until the centers are set but still slightly jiggly. Remove from the oven and let cool in the pan for 10 minutes.
Carefully remove the mini cheesecakes from the muffin tin and transfer them to a wire rack to cool completely. Refrigerate for at least 2 hours before serving.