Step 1: Preheat oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners.
Step 2: In a medium bowl, combine brownie mix, oil, 1 egg, and water. Stir until just combined.
Step 3: Divide brownie batter evenly among the muffin cups, about 1 tablespoon each.
Step 4: Bake for 10 minutes until brownie bases are set but not fully cooked.
Step 5: While brownies bake, beat cream cheese and sugar in a large bowl until smooth.
Step 6: Add 2 eggs and vanilla extract, mixing until fully incorporated.
Step 7: Stir in cooled melted chocolate until cheesecake batter is uniform.
Step 8: Remove muffin tin from oven and spoon cheesecake batter over brownie bases, filling cups almost to the top.
Step 9: Return to oven and bake for 18-20 minutes until cheesecakes are set but still slightly jiggly in the center.
Step 10: Cool in pan for 30 minutes, then refrigerate for at least 2 hours before serving.