In a medium bowl, combine crushed Oreo cookies with melted butter. Press the mixture into the bottom and about 1 inch up the sides of a 9-inch springform pan to create the crust. Refrigerate for 20 minutes to firm up.
In a microwave-safe bowl, melt chocolate chips in 30-second intervals, stirring after each, until fully smooth. This should take about 90 seconds total.
In a stand mixer, beat softened cream cheese, sugar, and flour together until smooth and creamy. It's important to use softened cream cheese to ensure a lump-free texture.
Add the eggs one at a time, mixing thoroughly after each addition. With the mixer on low speed, slowly pour in the melted chocolate, then add the sour cream and vanilla extract. Mix until smooth and fully combined.
Pour the cheesecake filling into the chilled crust. Wrap the bottom of the springform pan with foil to prevent water from leaking in.
Prepare a water bath by placing the springform pan into a larger baking dish. Fill the outer dish with hot water, about halfway up the sides of the springform pan.
Bake in a preheated oven at 350°F (175°C) for 60 minutes. The cheesecake should be slightly jiggly in the center when done.
Once the baking time is up, crack the oven door about 4-5 inches and let the cheesecake cool for 2 hours inside the partially opened oven. This helps prevent cracks.
After cooling, transfer the cheesecake to the refrigerator and chill for 4-6 hours before slicing and serving.