Preheat the oven to 325°F and grease a 9-inch springform pan.
In a medium bowl, combine graham cracker crumbs and melted butter, then press into the bottom of the prepared pan to form a crust.
Bake the crust for 10 minutes, then remove from the oven and let cool.
In a large mixing bowl, beat the softened cream cheese with granulated sugar and vanilla extract until smooth.
Add the eggs one at a time, mixing well after each addition, then stir in the sour cream until fully combined.
Melt the chocolate chips in a microwave-safe bowl in 30-second intervals, stirring in between until smooth, then allow to cool slightly.
Fold the melted chocolate into the cream cheese mixture.
In a separate bowl, mix the brownie mix with ¼ cup of water until just combined.
Pour half of the cheesecake batter over the cooled crust, followed by dollops of the brownie batter, and swirl the brownie batter into the cheesecake with a knife.
Pour the remaining cheesecake batter on top and smooth it out.
Sprinkle rainbow sprinkles on top of the cheesecake.
Bake for 55-60 minutes or until the edges are set but the center is still slightly jiggly.
Turn off the oven and crack the door, letting the cheesecake cool in the oven for 1 hour.
Remove from the oven and refrigerate for at least 4 hours or overnight before serving.