Get Ready: Preheat your oven to 350°F (175°C). Lightly grease a 9.5-inch springform pan. Line the bottom and sides with parchment paper. Wrap the outside of the pan tightly with foil to prevent any leaks during baking. Set this aside.
Make the Simple Brownie Base: Gently melt the butter and 1/2 cup chocolate chips together. You can do this in a double boiler or carefully in the microwave. In a large bowl, whisk the melted chocolate mixture with vegetable oil, granulated sugar, and brown sugar until it's smooth. Stir in the vanilla extract and eggs, beating for about a minute until the mixture looks lighter in color. Sift in the cocoa powder, flour, and salt, then mix just until everything is combined. Pour this brownie batter into your prepared springform pan. Bake for 30 minutes, or until the brownie is just set. While it bakes, you can start on your cheesecake filling! Once baked, remove the pan from the oven and reduce the oven temperature to 325°F (160°C).
Prepare the Creamy Cheesecake Filling: In a large bowl, beat the softened cream cheese with a hand mixer until it's super smooth and lump-free. Add the granulated sugar and vanilla extract, beating until they are well combined. Mix in the eggs one at a time, making sure each egg is fully blended before adding the next. Don't forget to scrape down the bowl after each egg! Gently beat in the heavy cream and sour cream until they are just incorporated into the batter. Be careful not to overmix. Finally, fold in the mini chocolate chips by hand. Pour this creamy cheesecake batter directly over the warm brownie crust in your springform pan.
Bake to Perfection (with a Water Bath): Place your cheesecake pan inside a slightly larger pan. Then, place both of these pans into an even larger roasting pan. Carefully fill the largest pan with about an inch of hot water to create a water bath – this helps your cheesecake bake evenly and prevents cracks. Place it in the preheated oven and bake for 1 hour 20 minutes to 1 hour 30 minutes, or until the center of the cheesecake is just slightly jiggly, like firm Jell-O. If it wiggles all over, it needs a little more time. Turn off the oven and crack the door open slightly. Let the cheesecake cool in the oven for 1 to 2 hours until it reaches room temperature. Transfer the cooled cheesecake to the fridge to chill overnight – this is the secret for a perfectly set, delicious texture!
Whip Up a Chocolate Ganache Topping: In a microwave-safe bowl, combine 1 1/2 cups semi-sweet chocolate chips and 1 cup heavy cream. Microwave in 30-second intervals, stirring well after each, until the ganache is smooth and completely melted. Let it sit at room temperature until it thickens to a consistency that's easy to spread or pipe. You can speed this up by placing it in the fridge, but keep a close eye on it! Once thickened, pipe or spread the rich ganache over your chilled cheesecake. Store the finished cheesecake in the fridge until you're ready to serve this amazing homemade treat!